Research ArticleEvolutionary Game Theoretic Modeling and Repetition ofMedia Distributed Shared in P2P-Based VANET
Di Wu1 He Liu1 Yingrong Bi1 and Hongsong Zhu2
1 School of Computer Science and Technology Dalian University of Technology Dalian 116024 China2 Institute of Information Engineering Chinese Academy of Sciences Beijing 100093 China
Correspondence should be addressed to He Liu lh rivulet163com
Received 24 April 2014 Accepted 3 June 2014 Published 23 June 2014
Academic Editor Jianwei Niu
Copyright copy 2014 Di Wu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A significant challenge in vehicular networks is to efficiently provide multimedia services with the constraints of limited resourceshigh mobility opportunistic contact and service time requirements In order to guarantee the vehicle user satisfaction ofmultimedia service with the proliferation of the distributed peer-to-peer (P2P) cooperative transmission technologies P2P-basedVANEThas recently received a substantial amount of interest Using the P2P services thought and at the same time a set ofmethodsshould be designed to avoid the disadvantage of P2P system appearing in VANET Under such a presupposition in this paper westudy the media provisions in P2P-based VANET and present a repeated game ldquoMore Pay for More Work (RGMPMW)rdquo incentivemechanism based on service evaluation informationWe also propose evolutionary game-based veracity (EGV) gamemodel whichexploits evolutionary game to guarantee the multimedia service share veracity of all vehicles in VANET In addition we provideextensive simulation results that demonstrate the effectiveness of our proposed schemes
1 Introduction
The applications of peer-to-peer (P2P) networks have beengrowing at tremendous speed these past few years Anotherhot area in communication networks is wireless mobile adhoc networks which enable distributed nodes to communi-cate with each other without a central access point or base sta-tion [1] VANET is considered to be one of themost promisingtechniques for providing road safety and innovative mobileapplications With the proliferation of the distributed peer-to-peer (P2P) cooperative transmission technologies P2P-based VANET has recently received a substantial amountof interest [2ndash5] P2P-based VANET makes it possible toprovide large data heterogeneous media content for movingvehicles [3 5]Media service over vehicular networks is a veryinteresting topic as it can greatly bring benefit to our daily life[3 6 7] In VANET multimedia can be divided into severalclasses according to different service types For example piv-otal emergency media services such as road dangerous andhighway condition and parking information delay-sensitivemedia services such as live videos and videoconferencesmedia services which can be fulfilled at any time for example
music entertainment living services for example restaurantand hotel messages and so on
There are two communicationmodes in VANET vehicle-to-vehicle (V2V) communications and communicationbetween vehicles and roadside units (RSU) (V2R) Figure 1shows the typical media service architecture for VANETwhich contains three parts namely a vehicular internetworka network provider and a content provider [8] In the vehicu-lar communications part a vehicle accesses the RSUs viadirect V2R communications when the vehicle enters into thecoverage of the RSU or via multihop V2V communicationswhen the vehicle is out of the RSUrsquos coverage In the networkprovider part RSUs act as Internet gateways to link vehiclesand media service providers [9] The media servers in thecontent provider part possess different media service data-bases With regard to P2P-based service fashion all vehiclesthemselves request media services and help provide mediaservices to others when they meet each other within the V2Vtransmission range
The architecture shown in Figure 1 due to the limitedbudget and high maintenance cost is difficult to deploy
Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014 Article ID 718639 14 pageshttpdxdoiorg1011552014718639
2 International Journal of Distributed Sensor Networks
Internet
RSU
V2RV2V
Figure 1 Media service architecture in VANET
a large amount of RSU (such as 80211 base stations) to coverthe complicated road areas [10] The introduction of V2Vconnectivity has fostered a number of proposals to exploitthe cooperation among vehicular users so as to improvetheir downloading performance In particular V2V-basedapproaches are especially attractive when one considers thatthe infrastructure coverage will be spotty at initial stages[11] In addition owing to the real-time and effectiveness ofmultimedia service and the mobility of vehicles is restrictedby the road directions as well as by traffic regulations Alsonetwork nodes (ie vehicles) tend to form groups whosebehaviors depend on the close-by nodes Since vehiclesmay join and leave the network at any time the networkcannot depend on a single vehicle for media forwarding [12]Therefore V2V communication is necessary as well as veryessential media service method in VANET
The specific features of V2V communications are allow-ing the deployment of a broad gamut of possible applicationsincluding traffic control road safety and in-car entertain-ment At the basis of all this lies the improvements of VANET-based transmission techniques that are becoming techno-logically mature [13] However intrinsic incentive problemsreside in P2P-based VANET as the transfer of media incurscosts both to suppliers and to requesters while the benefitaccrues only to requesters [14] Moreover malicious vehicleusers can also utilize the forwarding behavior to launchattacks if there is no cost To bring the VANET to theirfull potential an incentive scheme needs to be developedand employed according to the unique features of VANETand potential applications to stimulate cooperation [15]
Some incentive mechanisms had been studied in P2P systemand VANET Reference [16] studied a repeated game-basedincentivemechanism of bandwidth employing a trusted thirdparty to record peersrsquo contribution in each round of P2Psystem Reference [17] proposed an incentive mechanismbased on coalitional games which makes the vehicle userselect better route improves the ratio of delivery and reducesthe delay Reference [18] uses Reed-Solomon codes (RS-codes) to construct our incentive scheme and enhance itssecurity by introducing one discrete logarithm representationproblem to guarantee the vehicles cooperation in VANETHowever the incentive mechanisms in these papers studiedeither not apply to VANET or stimulate forwarding withcompleted compute Unlike these in this paper under themedia provision in P2P-based VANET we exploit littlefeedback information to present a RGMPMW incentivemechanism to stimulate vehicles share their multimedia inV2V communication
VANET is a kind of autonomic networks and the vehiclesin VANET are limited rationality at most cases [19] Underthe action of RGMPMW incentive mechanism vehicles mayexaggerate their contributions to get the most profits Herethe exaggeration of service contribution contains the follow-ing (a) vehicles exaggerate their service contributions to getmost profits (b) actions of malicious vehicles exaggeratingtheir service contributions intentionally to reduce the profitsof competitors Reference [16] solved the honest problemusing trusted third party However in VANET each vehicleis an independent node However in VANET each vehicleis equipped with a node Nodes from different vehicles cancommunicate but each node manages itself and is in chargeof its own service contribution in VANET Guaranteeing theveracity of this autonomous network is a challenging problembecause there is no central and trustedmanager to protect thewhole networkThus only distributedmechanisms are viablein autonomous networks such as VANET Evolutionary gametheory is used to the model where players have limited ratio-nality in the game thus it is suitable to analysis vehicles withlimited rationality so we can use evolutionary game theoryto investigate modelThe application of evolutionary game innetwork is popular in recent years [20ndash25] Therefore in thispaper we propose EGV game model to prevent vehicles arenot veracity improve the stability of system and ensure thevalidity of the mechanism
Therefore considering the specific characteristic of mul-timedia in P2P-based VANET this paper mainly studies thefollowing several aspects
(1) In P2P-based VANET we present a RGMPMWincentive mechanism based on the information ofservices evaluation Repeated game is exploited toaccurately evaluate the service contribution of eachvehicle in every game stage stimulating vehicles toshare their multimedia in V2V communication
(2) Based on evolutionary game propose EGV gamemodel to expand RGMPMW incentive mechanismof media Regarding the several vehicles that requestthe same supplier in the VANET as a populationprevent the mendacious service share of vehicles
International Journal of Distributed Sensor Networks 3
efficiently and guarantee service contribution veracityof vehicles in each stage game by evolving of singlepopulation
The target of this paper is to present a RGMPMWincentive mechanism based on the information of servicesevaluation to stimulate vehicles sharing their multimediabased on evolutionary game propose EGV game model toprevent the mendacious service share of vehicles efficientlyand guarantee service contribution veracity of vehicles ineach stage game by evolving of single population in P2P-based VANET
The rest of the paper is organized as follows Relatedwork on evolutionary game and repeated game are presentedin Section 2 Section 3 is system model Section 4 describesfeedback-based REGMPMW incentives scheme Evolution-ary game-based model for veracity of vehicles is reported inSection 5 Section 6 studies the simulation and analysis Weconclude our paper and propose perspectives in Section 7
2 Related Work
Game theory is a mathematical theory and method ofresearching the phenomenon with wrestled or competitiveproperty and under certain restricted conditions the partici-pators can implement strategies to other players tomake surethat the profits of participators reach a final balanced state
21 Evolutionary Game Classical game theory generallyassumes that each individual acts so as to maximize its utilityassuming that the others do the same and understandingcompletely the possible utility payoffs of their interactionsAn alternative perspective from evolutionary game theoryassumes that individuals will copy the behavior of otherswho obtain a higher utility [22] Evolutionary game hastwo core theories evolutionary stable strategy and replicatordynamics equation Evolutionary stable strategy emphasizesthe process of how a dynamic evolution system reaches asteady state and evolutionary stable strategy119909
lowast needs tomeetthe following two conditions first 1199091015840 = Ω(119909
lowast
) = 0 secondΩ1015840
(119909lowast
) lt 06 Replicator dynamic equation describes a
dynamic differential equation on time parameter 119905 taking thenumber of frequency variation Replicator dynamic equationis expressed by 119909
1015840
119894= [120601(119909
119894 119909) minus 120601(119909 119909)]119909
119894 where 119909
119894(119905) is the
proportion of participators who take pure strategy 120601(119909119894 119909) is
the fitness of strategy 119894 and 120601(119909 119909) is the average fitness ofstrategy 119894 [26]
The following describes the standard set of evolutionarygame theory [27]
(1) There is a group of users and the number of the usersin the group is very large
(2) Assuming that pure strategy or action exists Eachmember in the group chooses the strategy from thesame strategy set 119860 = 1 2 119868
(3) Let 119872 = (1199101 119910
119868) | 119910119895
ge 0 sum119868
119895=1119910119895
= 1 bethe possibility distribution set on pure strategy set119868 119872 can be interpreted as a mixed strategy set In
fact assuming that picking the user randomly fromthe group the possibility that the user with markedsign meets the user with strategy 119910 is 119910
119895 After a
few game processes participators who use strategy119895 is equivalent to the face using a mixed strategy ofparticipators
Evolutionary game in network application is very pop-ular and a currently [20ndash25 28] used evolutionary gameto solve the problem of uncooperative two-hop routingmessage forwarding control inDTN (delay tolerant network)Reference [21] used the mathematical framework of gametheory and evolutionary game theory for modeling clearlydemonstrating the connection of cooperation trust privacyand security in a multihop network in order to prevent thefake nodes prevent misuse detect anomalies and to protectusersrsquo privacy Reference [22] studied the resource allocationand the establishment of distribution tree Assuming thatthe allocation of video is based on a multiple descriptionencoder then using evolutionary game can significantlyaffect the scalability fast adaptation twist high degree ofnode cooperation and the autonomous of distributed nodetree network Reference [23] studied an energy manage-ment of stochastic evolutionary game in distributed alohanetwork Each participator may be in different states andcan be involved in the same local interaction during itslifetime Its action decides not only effectiveness but also thetransmission probability and the time of his life Reference[24] analyzed the problem of network dynamic selectionwith evolutionary game in heterogeneous wireless networksIt can guarantee the network performance in the case ofmultipopulation evolutionary game competition References[25] studied the evolutionary game based on the credibilityto forward data safely and deny the service attacks makingsure that the maximum numbers of nodes in the networkforward cooperatively in the autonomous ad hoc and sensornetwork
In P2P-based VANET vehicles move at high speed andinstant contribution is more important therefore in everyrequest slot 119905 each vehicle needs to decide how many mediaservices to share with the request vehicle This decision willaffect its profit in the next stageThus it is reasonable tomodelthe action of vehicles as repeated game
22 Repeated Game Repeated game means the same struc-ture game is repeated for many times where each game iscalled ldquostage gamerdquo Repeated game is an important part ofa dynamic game and it can repeat complete information orincomplete information When the game is executed onlyonce each participator just cares about one-time paymentBut if the game is repeated participators may tend to getlong- term profit instead of immediate profit thereforethey will choose a different equilibrium strategy Thus therepeat number will affect the outcome of equilibrium gameRepeated game has three basic characteristics (a) In therepeated game stage there is no ldquosubstancerdquo connectionbetween games that is to say that the previous stage of thegamewill not change the construction of the next stage (b) Inevery stage of the repeated game all participators can observe
4 International Journal of Distributed Sensor Networks
the history of the game (c) Total profit of participators isthe discounted value sum or weighted average number of allstagesrsquo profit
Repeated game in network application has also beenstudied widely [16 29ndash32] Reference [16] proposed serverdifferentiation incentives for P2P streaming system based onthe immediate profit of nodes At the same time it designeda repeated game model to analyze how much should everynode contribute in every round in this incentive Reference[29] used repeated game theory in FiWi access networkand applied effective quality service routing mechanisms andscheduling policy into practical application Balance strategyguaranteed the quality of service of FiWi wireless networkReference [30] used repeated game model to establish alimited punishment mechanism to enforce selfish nodes tobe unselfish preventing cheating to save energy Reference[31] checked some basic important properties of a rout-ing protocol design The importance of these attributes isautonomous participators from the underlying economicfactorsrsquo management behaviorThe connected price informa-tion in an associated swap is regarded as a repeated gameamong the relevant participators Reference [32] studied themulticast overlay network applications in the framework ofrepeated games and described a repeated gamemodel of userbehaviors to capture the effect of short-term profit to long-term profit
VANET is an autonomous network and participators aregroups or individuals with limited rationality Traditionalgame theory methods assume that participators are entirelyrational Evolutionary game theory is a game addressing nodebounded rationality specifically Therefore it is reasonablethat we use evolutionary game as a research method in thispaper
3 System Model
In VANET there are two main ways of communicationvehicle to vehicle (V2V) and vehicle to RSU (V2R) In theanalysis of part I we only consider V2V communicationunder urban scenes We regard VANET as a network ofvehiclesrsquo set and each vehicle is equipped with communica-tion equipment allowing communication based on 80211pprotocol among different vehicles As is shown in Figure 1nodes begin to download the initial service from RSU thenwhen the vehicle is moving out of the range of RSU servicesIn order to obtain a satisfactory quality of service V2Vcommunication is needed in RSU communication blackoutConsidering a typical P2P-based VANET multimedia ser-vices under urban scenes at a certain time the role of eachvehicle is ldquoRequesterrdquo (ask for service) or ldquoSupplierrdquo (provideservice) As a requester it may face several suppliers withsame services as a supplier it may also face more than onerequester
The ldquoMore Pay for More Work (RGMPMW)rdquo incentivemechanism and EGV game model are used into the urbanVANET with double lane in this paper and the incentive
mechanism performs well The models in the paper areintroduced as follows
31 The Model of Vehicles Encounter VANET is a networkcollection of vehicles 119881 = 1 2 119894 Each vehicle can joinor leave the network at any timeThe running speed of vehicleis V119894 119894 = 1 2 |119881| isin (5 16)ms We use 119889
119894119895isin (1 5000)
to express the distance between vehicle 119894 and vehicle 119895 andthe chance of encounter between vehicles is independentwithno interfering Here we define vehicles that meet within eachtransmission range Assuming the transmission range of theevery vehicle is 250m The probability that vehicle 119894 andvehicle 119895 meet is expressed as 119902
119894119895
119902119894119895
=
V119894minus V119895
005 lowast 119889119894119895
same running direction vehicle 119894 is
behind vehicle 119895 V119894gt V119895
119889119894119895
isin (250 5000)
0 leaving in opposite directionor same runnig directionvehicle 119894 is behind vehicle 119895
V119894lt V119895 119889119894119895
isin (250 5000)
1 move in opposite direction119889119894119895
isin (250 5000) or 119889119894119895
isin (1 250)
(1)
As is shown in Figure 2(a) in the period 119905 minus 1 vehicle 2has the media service which vehicle 1 vehicle 5 and vehicle6 need then they make a service request to vehicle 2 Atthis time node 2 can be regarded as a similar manager ofnodes 1 2 5 and 6 In the next period 119905 there are two vehiclenodes 7 and 8 added into network At this time vehicles5 and 6 run out of the communication range of vehicle 2therefore they make media request from vehicle 7 Vehicle1 and vehicle 2 are running in the same direction so theycan still continue to keep connection At this time vehicle2 loses manage capabilities of vehicles 5 and 6 and vehicle7 becomes the current similar manager of vehicles 5 and 6vehicle 2 becomes the similar manager of vehicles 1 2 4and 8 With the movement of vehicles every vehiclersquos similarmanager is changing in other words the connected timebetween vehicles is not fixed Figure 2 is just a simplifiedmodel only showing a partial service communication In factevery vehicle is a similar manager of a group In this paperwe only consider the situation of one provider and severalrequesters
Because of the mobility of vehicles in VANET it isimpossible to choose a fixed reliable third-party to managea certain number of nodes For simplicity first we assumethat (1) nodes in VANET have their own media services(2) initially each vehicle gets a certain amount of mediaservices from the RSU and gets initialized with a certaincontribution value when entering the network (3) the mediaservice among vehicles is instantaneous and there is no timelimit (4) at the time every vehicle enter the network it is given
International Journal of Distributed Sensor Networks 5
1
2
3
4
5
6
(a) 119905 minus 1
12
3
4
5
6
7
8
(b) 119905
Figure 2 The model of vehicles encounter
a unique real identity (5) the transmission range of vehiclesis the same
32Media ServiceModel In this paper we dividemultimediaservices into four kinds based on the type and popularityof the media (1) critical urgent media services such asroad hazard information and highway information definedas 119875119894(119905) = 09 (2) delay-sensitive services [33] such as
video conference and video service defined as 119875119894(119905) = 07
(3) constantly completed multimedia services like musicentertainment defined as 119875
119894(119905) = 05 (4) life services such
as restaurant hotel information service defined 119875119894(119905) = 02
where 119875119896(119905) represents the popularity of the media provided
by providers in the current stage of the game 119875119896(119905) isin [0 1]
When requesters ask for media service from providerthey will give their shared value of the previous phase to theprovider Since vehicles have a strong ability of computingprovider will determine the allocation of resources based onthe shared value of all requesters Meanwhile at the end ofthe request requesters will broadcast information to all nodesin the network such as information about media serviceprovider and value (Section 4 will describe evaluation ofmedia service in detail) Therefore all nodes in network willstore a list record ID and shared value of all nodes in thenetwork For nodes that just enter the network they will get aunique ID and thenwhen theymeet first node they will copyall records from it to complete information All nodes updaterecords in each time slot
4 Offer-Based RGMPMW Incentives Scheme
Since vehicle nodes in VANET are naturally selfish theywill not go to contribute their resources to other peer nodeswithout motive Therefore we need to design an incentivemechanism to encourage the contribution of nodes [17]
In the P2P-based VANET design of incentivemechanismshould consider instant contribution of vehicles Taking real-time requirement of media streams into account the vehicles
are more strictly required to share their resources in everyround otherwise the requester may not receive the databefore the playback time When implementing incentivemechanism to nodes contribution of current time periodis more important than historical contribution Repeatedgame keeping encouraging nodes to contribute includes alot of repeated game stages of participators In each stagethe decisions of participators all depend on their paymentAn action can be determined by one participator giving itthe highest payment Therefore in the repeated game whenparticipators decide what strategy to take they must careabout current and future payment [29]This paper proposes aRGMPMW incentivemechanism based on similarmanagers
In this incentive mechanism we define a noun ldquosharedcontribution valuerdquo representing the contribution of a nodemade in a game stage It is related to bandwidth popularity ofthemedia and amount of providers of nodesrsquo contribution Inthe sharing mechanism ldquoshared contribution valuerdquo of nodesis evaluated by uploaddownload behavior in a previous stageEach node broadcasts evaluation of servicersquos popularity andimportance before the end of the game In the same stageevery provider is a similar manager and it decides requestersrsquoprofit in current stage based on ldquoshared contribution valuerdquoof previous stage provided by requesters
Therefore the ldquoshared contribution valuerdquo of a node kinstage 119905 is the sum of feedback information provided by allnodes that received the media service of 119896 That is
119881119896(119905) =
119899
sum
119894=1
119862119894(119905) lowast 119875
119894(119905) (2)
For simplicity we assume that the system model in thispaper is that every vehicle node in a slot 119905 provides only onekind of media service Thus the ldquoshared contribution valuerdquoof a node 119896 in slot 119905 can be simplified as
119881119896(119905) = 119862
119896(119905) lowast 119875
119896(119905) (3)
where 119881119896(119905) represents ldquoshared contribution valuerdquo 119862
119896(119905)
represents bandwidth contributed by 119878 and 119875119896(119905) represents
6 International Journal of Distributed Sensor Networks
Figure 3 The model of vehicle requesting
the popularity of the media provided by 119878 in current stage119875119896(119905) isin [0 1]Figure 2 shows the system model of communications
among vehicles under urban scenes in VANET A vehiclemay be both a service provider and a service requester ina stage of the game However in the incentive mechanismproposed in this paper we are most concerned about theldquoshared contribution valuerdquo Here we only consider a simplescenario one provider corresponds to several requesters asis shown in Figure 3
In vehicle request model when a vehicle asks for mediaservices it will give its ldquoshared contribution valuerdquo in previousstage to provider and provider will determine the allocationof resources based on the shared value of all requesters Wedefine the resource assigned from provider 119878 to a requester intime 119905 which is
119866119904119894
(119905) = 119902119894119904
lowast 119866119904lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
(4)
where 119902119894119904
is the meet probability of two vehicles and it isrelated to their the running speed and distance 119866
119904is the
contribution set by provider 119878 in current stage 119881119894(119905 minus 1) is
the ldquoshared contribution valuerdquo of requester 119894 in previousstage 119881
minus119894(119905 minus 1) is the sum ldquoshared contribution valuerdquo of all
requesters except requester 119894Therefore the profit function ofeach node is the difference between the service obtained byprovider and the total service it provides for other requesters
119906119894(119905) = 119866
119904119894(119905) minus 119881
119894(119905) (5)
As vehicle node is autonomous the service media type isdecided by each node In order to obtain greater payoff eachnode tends to choose high popularity of media services We
set119866119904= 119881119904(119905minus1) Then the utility function of requestor 119894 can
be rewritten as
119906119894(119905) = 119902
119894119904lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(6)
In addition we define the total utility of node 119894 in theservice time as follows
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
119906119894(119905) (7)
Here 120575 isin (0 1] is the discount factor and it can beregarded as a nodersquos patience for the subsequent game Thegreater the value is themore patient node is On the contrarythe node will pay more attention to the current earnings Inthe infinite repeated game every participant does not knowwhen the game will end So we assume that the probability ofthe end of the game is 119901
The implementation steps of RGMPMW incentivemechanism based on similar management are shown inAlgorithm 1
We can get from formulas (6) and (7) the following
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast 119902119894119904
lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(8)
The goal of the node 119894 is to maximize 119906(119894) First we canget the formula (9) by a series of deformation for the formula(7)
119906 (119894) =
119881119904(0)
119881119894(0) + 119881
minus119894(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119894(119905)
119881119894(119905) + 119881
minus119894(119905)
minus 119881119894(119905)
(9)
where 119881119896(0) is the initialization ldquoshared contribution valuerdquo
when the node 119896 comes into the network at the beginning So119881119904(0)(119881
119894(0) + 119881
minus119894(0)) is a constant After deformation each
item is independent in the sum Therefore we can make thesum maximized by maximizing each item
We set119889 ([120575 (1 minus 119901)] lowast 119902
where 119899 is the number of vehicles requesting node 119878Putting the formula (14) to the formula (12) we can get
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
1198992
=
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904
(15)
The payoff of the node will be maximized when theequation above equation is established
5 Evolutionary Game Model forVeracity of Vehicles
In Section 4 the function of RGMPMW incentives schemebased on information is when the node is rational it willactively share its media resource to gain more payoffs But inVANETwhich is autonomic network it is not practical for thenode to be completely rational In the process of each gameif each requestorrsquos ldquoshared contribution valuerdquo is stable atpresent namely node ldquoshared contribution valuerdquo fluctuation
is small he will get unexpected payoff when one requesterexaggerates his previous contribution or there are attacksof malicious nodes which exaggerate their contributiondeliberately and make the payoffs low So we should studynode bounded rationality in VANET and the situation thatthe nodes do not trust each other In this section we presentan EGV game model by using a game theory which can beapplied to the node bounded rationality which can preventthe node exaggerating its ldquoshared contribution valuerdquo togain extra payoff or malicious attacks and to guarantee theauthenticity of all the nodes
51 Structure and Solution of Evolutionary Game In thispaper we set the vehicles which request for the same vehicleas an evolutionary group Researching on evolutionary gametheory amutation of disadvantage group is the vehicleswhichexaggerate their own shared services for more payoffs andreduce the payoff of the other competitors After a longevolution disadvantage groupwill be eliminated and vehiclesrsquoreal ldquoshared contribution valuerdquo will be guaranteedWe knowthat in the real network the exaggerated nodes will benefitmore because it means that in the case the other nodes arereal the exaggerated nodes will get more in the next round ofthe game
In VANET based on P2P vehicles provide service for eachother In each stage in the game all the vehicles will broadcasttheir gains So all the vehicles in the network will receive thebroadcast information and accumulate the value accordingto the identity of the vehicles At the end of the stage gameeach vehicle records the stage game information (vehicleidentification total service) of all the vehicles in the networkTherefore the vehicles will refuse to provide service when thenodes choose ldquoexaggeratorrdquo according to their record
In evolutionary game the game of the participants istwo random vehicle nodes Suppose in the whole population
8 International Journal of Distributed Sensor Networks
Table 1 Pay-off matrix
Participant 119894Real Exaggerator
119895
Real 119906(119894) 119906(119895) 119906(119894) + 120572119891 minus119881119895(119905)
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
2 International Journal of Distributed Sensor Networks
Internet
RSU
V2RV2V
Figure 1 Media service architecture in VANET
a large amount of RSU (such as 80211 base stations) to coverthe complicated road areas [10] The introduction of V2Vconnectivity has fostered a number of proposals to exploitthe cooperation among vehicular users so as to improvetheir downloading performance In particular V2V-basedapproaches are especially attractive when one considers thatthe infrastructure coverage will be spotty at initial stages[11] In addition owing to the real-time and effectiveness ofmultimedia service and the mobility of vehicles is restrictedby the road directions as well as by traffic regulations Alsonetwork nodes (ie vehicles) tend to form groups whosebehaviors depend on the close-by nodes Since vehiclesmay join and leave the network at any time the networkcannot depend on a single vehicle for media forwarding [12]Therefore V2V communication is necessary as well as veryessential media service method in VANET
The specific features of V2V communications are allow-ing the deployment of a broad gamut of possible applicationsincluding traffic control road safety and in-car entertain-ment At the basis of all this lies the improvements of VANET-based transmission techniques that are becoming techno-logically mature [13] However intrinsic incentive problemsreside in P2P-based VANET as the transfer of media incurscosts both to suppliers and to requesters while the benefitaccrues only to requesters [14] Moreover malicious vehicleusers can also utilize the forwarding behavior to launchattacks if there is no cost To bring the VANET to theirfull potential an incentive scheme needs to be developedand employed according to the unique features of VANETand potential applications to stimulate cooperation [15]
Some incentive mechanisms had been studied in P2P systemand VANET Reference [16] studied a repeated game-basedincentivemechanism of bandwidth employing a trusted thirdparty to record peersrsquo contribution in each round of P2Psystem Reference [17] proposed an incentive mechanismbased on coalitional games which makes the vehicle userselect better route improves the ratio of delivery and reducesthe delay Reference [18] uses Reed-Solomon codes (RS-codes) to construct our incentive scheme and enhance itssecurity by introducing one discrete logarithm representationproblem to guarantee the vehicles cooperation in VANETHowever the incentive mechanisms in these papers studiedeither not apply to VANET or stimulate forwarding withcompleted compute Unlike these in this paper under themedia provision in P2P-based VANET we exploit littlefeedback information to present a RGMPMW incentivemechanism to stimulate vehicles share their multimedia inV2V communication
VANET is a kind of autonomic networks and the vehiclesin VANET are limited rationality at most cases [19] Underthe action of RGMPMW incentive mechanism vehicles mayexaggerate their contributions to get the most profits Herethe exaggeration of service contribution contains the follow-ing (a) vehicles exaggerate their service contributions to getmost profits (b) actions of malicious vehicles exaggeratingtheir service contributions intentionally to reduce the profitsof competitors Reference [16] solved the honest problemusing trusted third party However in VANET each vehicleis an independent node However in VANET each vehicleis equipped with a node Nodes from different vehicles cancommunicate but each node manages itself and is in chargeof its own service contribution in VANET Guaranteeing theveracity of this autonomous network is a challenging problembecause there is no central and trustedmanager to protect thewhole networkThus only distributedmechanisms are viablein autonomous networks such as VANET Evolutionary gametheory is used to the model where players have limited ratio-nality in the game thus it is suitable to analysis vehicles withlimited rationality so we can use evolutionary game theoryto investigate modelThe application of evolutionary game innetwork is popular in recent years [20ndash25] Therefore in thispaper we propose EGV game model to prevent vehicles arenot veracity improve the stability of system and ensure thevalidity of the mechanism
Therefore considering the specific characteristic of mul-timedia in P2P-based VANET this paper mainly studies thefollowing several aspects
(1) In P2P-based VANET we present a RGMPMWincentive mechanism based on the information ofservices evaluation Repeated game is exploited toaccurately evaluate the service contribution of eachvehicle in every game stage stimulating vehicles toshare their multimedia in V2V communication
(2) Based on evolutionary game propose EGV gamemodel to expand RGMPMW incentive mechanismof media Regarding the several vehicles that requestthe same supplier in the VANET as a populationprevent the mendacious service share of vehicles
International Journal of Distributed Sensor Networks 3
efficiently and guarantee service contribution veracityof vehicles in each stage game by evolving of singlepopulation
The target of this paper is to present a RGMPMWincentive mechanism based on the information of servicesevaluation to stimulate vehicles sharing their multimediabased on evolutionary game propose EGV game model toprevent the mendacious service share of vehicles efficientlyand guarantee service contribution veracity of vehicles ineach stage game by evolving of single population in P2P-based VANET
The rest of the paper is organized as follows Relatedwork on evolutionary game and repeated game are presentedin Section 2 Section 3 is system model Section 4 describesfeedback-based REGMPMW incentives scheme Evolution-ary game-based model for veracity of vehicles is reported inSection 5 Section 6 studies the simulation and analysis Weconclude our paper and propose perspectives in Section 7
2 Related Work
Game theory is a mathematical theory and method ofresearching the phenomenon with wrestled or competitiveproperty and under certain restricted conditions the partici-pators can implement strategies to other players tomake surethat the profits of participators reach a final balanced state
21 Evolutionary Game Classical game theory generallyassumes that each individual acts so as to maximize its utilityassuming that the others do the same and understandingcompletely the possible utility payoffs of their interactionsAn alternative perspective from evolutionary game theoryassumes that individuals will copy the behavior of otherswho obtain a higher utility [22] Evolutionary game hastwo core theories evolutionary stable strategy and replicatordynamics equation Evolutionary stable strategy emphasizesthe process of how a dynamic evolution system reaches asteady state and evolutionary stable strategy119909
lowast needs tomeetthe following two conditions first 1199091015840 = Ω(119909
lowast
) = 0 secondΩ1015840
(119909lowast
) lt 06 Replicator dynamic equation describes a
dynamic differential equation on time parameter 119905 taking thenumber of frequency variation Replicator dynamic equationis expressed by 119909
1015840
119894= [120601(119909
119894 119909) minus 120601(119909 119909)]119909
119894 where 119909
119894(119905) is the
proportion of participators who take pure strategy 120601(119909119894 119909) is
the fitness of strategy 119894 and 120601(119909 119909) is the average fitness ofstrategy 119894 [26]
The following describes the standard set of evolutionarygame theory [27]
(1) There is a group of users and the number of the usersin the group is very large
(2) Assuming that pure strategy or action exists Eachmember in the group chooses the strategy from thesame strategy set 119860 = 1 2 119868
(3) Let 119872 = (1199101 119910
119868) | 119910119895
ge 0 sum119868
119895=1119910119895
= 1 bethe possibility distribution set on pure strategy set119868 119872 can be interpreted as a mixed strategy set In
fact assuming that picking the user randomly fromthe group the possibility that the user with markedsign meets the user with strategy 119910 is 119910
119895 After a
few game processes participators who use strategy119895 is equivalent to the face using a mixed strategy ofparticipators
Evolutionary game in network application is very pop-ular and a currently [20ndash25 28] used evolutionary gameto solve the problem of uncooperative two-hop routingmessage forwarding control inDTN (delay tolerant network)Reference [21] used the mathematical framework of gametheory and evolutionary game theory for modeling clearlydemonstrating the connection of cooperation trust privacyand security in a multihop network in order to prevent thefake nodes prevent misuse detect anomalies and to protectusersrsquo privacy Reference [22] studied the resource allocationand the establishment of distribution tree Assuming thatthe allocation of video is based on a multiple descriptionencoder then using evolutionary game can significantlyaffect the scalability fast adaptation twist high degree ofnode cooperation and the autonomous of distributed nodetree network Reference [23] studied an energy manage-ment of stochastic evolutionary game in distributed alohanetwork Each participator may be in different states andcan be involved in the same local interaction during itslifetime Its action decides not only effectiveness but also thetransmission probability and the time of his life Reference[24] analyzed the problem of network dynamic selectionwith evolutionary game in heterogeneous wireless networksIt can guarantee the network performance in the case ofmultipopulation evolutionary game competition References[25] studied the evolutionary game based on the credibilityto forward data safely and deny the service attacks makingsure that the maximum numbers of nodes in the networkforward cooperatively in the autonomous ad hoc and sensornetwork
In P2P-based VANET vehicles move at high speed andinstant contribution is more important therefore in everyrequest slot 119905 each vehicle needs to decide how many mediaservices to share with the request vehicle This decision willaffect its profit in the next stageThus it is reasonable tomodelthe action of vehicles as repeated game
22 Repeated Game Repeated game means the same struc-ture game is repeated for many times where each game iscalled ldquostage gamerdquo Repeated game is an important part ofa dynamic game and it can repeat complete information orincomplete information When the game is executed onlyonce each participator just cares about one-time paymentBut if the game is repeated participators may tend to getlong- term profit instead of immediate profit thereforethey will choose a different equilibrium strategy Thus therepeat number will affect the outcome of equilibrium gameRepeated game has three basic characteristics (a) In therepeated game stage there is no ldquosubstancerdquo connectionbetween games that is to say that the previous stage of thegamewill not change the construction of the next stage (b) Inevery stage of the repeated game all participators can observe
4 International Journal of Distributed Sensor Networks
the history of the game (c) Total profit of participators isthe discounted value sum or weighted average number of allstagesrsquo profit
Repeated game in network application has also beenstudied widely [16 29ndash32] Reference [16] proposed serverdifferentiation incentives for P2P streaming system based onthe immediate profit of nodes At the same time it designeda repeated game model to analyze how much should everynode contribute in every round in this incentive Reference[29] used repeated game theory in FiWi access networkand applied effective quality service routing mechanisms andscheduling policy into practical application Balance strategyguaranteed the quality of service of FiWi wireless networkReference [30] used repeated game model to establish alimited punishment mechanism to enforce selfish nodes tobe unselfish preventing cheating to save energy Reference[31] checked some basic important properties of a rout-ing protocol design The importance of these attributes isautonomous participators from the underlying economicfactorsrsquo management behaviorThe connected price informa-tion in an associated swap is regarded as a repeated gameamong the relevant participators Reference [32] studied themulticast overlay network applications in the framework ofrepeated games and described a repeated gamemodel of userbehaviors to capture the effect of short-term profit to long-term profit
VANET is an autonomous network and participators aregroups or individuals with limited rationality Traditionalgame theory methods assume that participators are entirelyrational Evolutionary game theory is a game addressing nodebounded rationality specifically Therefore it is reasonablethat we use evolutionary game as a research method in thispaper
3 System Model
In VANET there are two main ways of communicationvehicle to vehicle (V2V) and vehicle to RSU (V2R) In theanalysis of part I we only consider V2V communicationunder urban scenes We regard VANET as a network ofvehiclesrsquo set and each vehicle is equipped with communica-tion equipment allowing communication based on 80211pprotocol among different vehicles As is shown in Figure 1nodes begin to download the initial service from RSU thenwhen the vehicle is moving out of the range of RSU servicesIn order to obtain a satisfactory quality of service V2Vcommunication is needed in RSU communication blackoutConsidering a typical P2P-based VANET multimedia ser-vices under urban scenes at a certain time the role of eachvehicle is ldquoRequesterrdquo (ask for service) or ldquoSupplierrdquo (provideservice) As a requester it may face several suppliers withsame services as a supplier it may also face more than onerequester
The ldquoMore Pay for More Work (RGMPMW)rdquo incentivemechanism and EGV game model are used into the urbanVANET with double lane in this paper and the incentive
mechanism performs well The models in the paper areintroduced as follows
31 The Model of Vehicles Encounter VANET is a networkcollection of vehicles 119881 = 1 2 119894 Each vehicle can joinor leave the network at any timeThe running speed of vehicleis V119894 119894 = 1 2 |119881| isin (5 16)ms We use 119889
119894119895isin (1 5000)
to express the distance between vehicle 119894 and vehicle 119895 andthe chance of encounter between vehicles is independentwithno interfering Here we define vehicles that meet within eachtransmission range Assuming the transmission range of theevery vehicle is 250m The probability that vehicle 119894 andvehicle 119895 meet is expressed as 119902
119894119895
119902119894119895
=
V119894minus V119895
005 lowast 119889119894119895
same running direction vehicle 119894 is
behind vehicle 119895 V119894gt V119895
119889119894119895
isin (250 5000)
0 leaving in opposite directionor same runnig directionvehicle 119894 is behind vehicle 119895
V119894lt V119895 119889119894119895
isin (250 5000)
1 move in opposite direction119889119894119895
isin (250 5000) or 119889119894119895
isin (1 250)
(1)
As is shown in Figure 2(a) in the period 119905 minus 1 vehicle 2has the media service which vehicle 1 vehicle 5 and vehicle6 need then they make a service request to vehicle 2 Atthis time node 2 can be regarded as a similar manager ofnodes 1 2 5 and 6 In the next period 119905 there are two vehiclenodes 7 and 8 added into network At this time vehicles5 and 6 run out of the communication range of vehicle 2therefore they make media request from vehicle 7 Vehicle1 and vehicle 2 are running in the same direction so theycan still continue to keep connection At this time vehicle2 loses manage capabilities of vehicles 5 and 6 and vehicle7 becomes the current similar manager of vehicles 5 and 6vehicle 2 becomes the similar manager of vehicles 1 2 4and 8 With the movement of vehicles every vehiclersquos similarmanager is changing in other words the connected timebetween vehicles is not fixed Figure 2 is just a simplifiedmodel only showing a partial service communication In factevery vehicle is a similar manager of a group In this paperwe only consider the situation of one provider and severalrequesters
Because of the mobility of vehicles in VANET it isimpossible to choose a fixed reliable third-party to managea certain number of nodes For simplicity first we assumethat (1) nodes in VANET have their own media services(2) initially each vehicle gets a certain amount of mediaservices from the RSU and gets initialized with a certaincontribution value when entering the network (3) the mediaservice among vehicles is instantaneous and there is no timelimit (4) at the time every vehicle enter the network it is given
International Journal of Distributed Sensor Networks 5
1
2
3
4
5
6
(a) 119905 minus 1
12
3
4
5
6
7
8
(b) 119905
Figure 2 The model of vehicles encounter
a unique real identity (5) the transmission range of vehiclesis the same
32Media ServiceModel In this paper we dividemultimediaservices into four kinds based on the type and popularityof the media (1) critical urgent media services such asroad hazard information and highway information definedas 119875119894(119905) = 09 (2) delay-sensitive services [33] such as
video conference and video service defined as 119875119894(119905) = 07
(3) constantly completed multimedia services like musicentertainment defined as 119875
119894(119905) = 05 (4) life services such
as restaurant hotel information service defined 119875119894(119905) = 02
where 119875119896(119905) represents the popularity of the media provided
by providers in the current stage of the game 119875119896(119905) isin [0 1]
When requesters ask for media service from providerthey will give their shared value of the previous phase to theprovider Since vehicles have a strong ability of computingprovider will determine the allocation of resources based onthe shared value of all requesters Meanwhile at the end ofthe request requesters will broadcast information to all nodesin the network such as information about media serviceprovider and value (Section 4 will describe evaluation ofmedia service in detail) Therefore all nodes in network willstore a list record ID and shared value of all nodes in thenetwork For nodes that just enter the network they will get aunique ID and thenwhen theymeet first node they will copyall records from it to complete information All nodes updaterecords in each time slot
4 Offer-Based RGMPMW Incentives Scheme
Since vehicle nodes in VANET are naturally selfish theywill not go to contribute their resources to other peer nodeswithout motive Therefore we need to design an incentivemechanism to encourage the contribution of nodes [17]
In the P2P-based VANET design of incentivemechanismshould consider instant contribution of vehicles Taking real-time requirement of media streams into account the vehicles
are more strictly required to share their resources in everyround otherwise the requester may not receive the databefore the playback time When implementing incentivemechanism to nodes contribution of current time periodis more important than historical contribution Repeatedgame keeping encouraging nodes to contribute includes alot of repeated game stages of participators In each stagethe decisions of participators all depend on their paymentAn action can be determined by one participator giving itthe highest payment Therefore in the repeated game whenparticipators decide what strategy to take they must careabout current and future payment [29]This paper proposes aRGMPMW incentivemechanism based on similarmanagers
In this incentive mechanism we define a noun ldquosharedcontribution valuerdquo representing the contribution of a nodemade in a game stage It is related to bandwidth popularity ofthemedia and amount of providers of nodesrsquo contribution Inthe sharing mechanism ldquoshared contribution valuerdquo of nodesis evaluated by uploaddownload behavior in a previous stageEach node broadcasts evaluation of servicersquos popularity andimportance before the end of the game In the same stageevery provider is a similar manager and it decides requestersrsquoprofit in current stage based on ldquoshared contribution valuerdquoof previous stage provided by requesters
Therefore the ldquoshared contribution valuerdquo of a node kinstage 119905 is the sum of feedback information provided by allnodes that received the media service of 119896 That is
119881119896(119905) =
119899
sum
119894=1
119862119894(119905) lowast 119875
119894(119905) (2)
For simplicity we assume that the system model in thispaper is that every vehicle node in a slot 119905 provides only onekind of media service Thus the ldquoshared contribution valuerdquoof a node 119896 in slot 119905 can be simplified as
119881119896(119905) = 119862
119896(119905) lowast 119875
119896(119905) (3)
where 119881119896(119905) represents ldquoshared contribution valuerdquo 119862
119896(119905)
represents bandwidth contributed by 119878 and 119875119896(119905) represents
6 International Journal of Distributed Sensor Networks
Figure 3 The model of vehicle requesting
the popularity of the media provided by 119878 in current stage119875119896(119905) isin [0 1]Figure 2 shows the system model of communications
among vehicles under urban scenes in VANET A vehiclemay be both a service provider and a service requester ina stage of the game However in the incentive mechanismproposed in this paper we are most concerned about theldquoshared contribution valuerdquo Here we only consider a simplescenario one provider corresponds to several requesters asis shown in Figure 3
In vehicle request model when a vehicle asks for mediaservices it will give its ldquoshared contribution valuerdquo in previousstage to provider and provider will determine the allocationof resources based on the shared value of all requesters Wedefine the resource assigned from provider 119878 to a requester intime 119905 which is
119866119904119894
(119905) = 119902119894119904
lowast 119866119904lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
(4)
where 119902119894119904
is the meet probability of two vehicles and it isrelated to their the running speed and distance 119866
119904is the
contribution set by provider 119878 in current stage 119881119894(119905 minus 1) is
the ldquoshared contribution valuerdquo of requester 119894 in previousstage 119881
minus119894(119905 minus 1) is the sum ldquoshared contribution valuerdquo of all
requesters except requester 119894Therefore the profit function ofeach node is the difference between the service obtained byprovider and the total service it provides for other requesters
119906119894(119905) = 119866
119904119894(119905) minus 119881
119894(119905) (5)
As vehicle node is autonomous the service media type isdecided by each node In order to obtain greater payoff eachnode tends to choose high popularity of media services We
set119866119904= 119881119904(119905minus1) Then the utility function of requestor 119894 can
be rewritten as
119906119894(119905) = 119902
119894119904lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(6)
In addition we define the total utility of node 119894 in theservice time as follows
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
119906119894(119905) (7)
Here 120575 isin (0 1] is the discount factor and it can beregarded as a nodersquos patience for the subsequent game Thegreater the value is themore patient node is On the contrarythe node will pay more attention to the current earnings Inthe infinite repeated game every participant does not knowwhen the game will end So we assume that the probability ofthe end of the game is 119901
The implementation steps of RGMPMW incentivemechanism based on similar management are shown inAlgorithm 1
We can get from formulas (6) and (7) the following
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast 119902119894119904
lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(8)
The goal of the node 119894 is to maximize 119906(119894) First we canget the formula (9) by a series of deformation for the formula(7)
119906 (119894) =
119881119904(0)
119881119894(0) + 119881
minus119894(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119894(119905)
119881119894(119905) + 119881
minus119894(119905)
minus 119881119894(119905)
(9)
where 119881119896(0) is the initialization ldquoshared contribution valuerdquo
when the node 119896 comes into the network at the beginning So119881119904(0)(119881
119894(0) + 119881
minus119894(0)) is a constant After deformation each
item is independent in the sum Therefore we can make thesum maximized by maximizing each item
We set119889 ([120575 (1 minus 119901)] lowast 119902
where 119899 is the number of vehicles requesting node 119878Putting the formula (14) to the formula (12) we can get
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
1198992
=
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904
(15)
The payoff of the node will be maximized when theequation above equation is established
5 Evolutionary Game Model forVeracity of Vehicles
In Section 4 the function of RGMPMW incentives schemebased on information is when the node is rational it willactively share its media resource to gain more payoffs But inVANETwhich is autonomic network it is not practical for thenode to be completely rational In the process of each gameif each requestorrsquos ldquoshared contribution valuerdquo is stable atpresent namely node ldquoshared contribution valuerdquo fluctuation
is small he will get unexpected payoff when one requesterexaggerates his previous contribution or there are attacksof malicious nodes which exaggerate their contributiondeliberately and make the payoffs low So we should studynode bounded rationality in VANET and the situation thatthe nodes do not trust each other In this section we presentan EGV game model by using a game theory which can beapplied to the node bounded rationality which can preventthe node exaggerating its ldquoshared contribution valuerdquo togain extra payoff or malicious attacks and to guarantee theauthenticity of all the nodes
51 Structure and Solution of Evolutionary Game In thispaper we set the vehicles which request for the same vehicleas an evolutionary group Researching on evolutionary gametheory amutation of disadvantage group is the vehicleswhichexaggerate their own shared services for more payoffs andreduce the payoff of the other competitors After a longevolution disadvantage groupwill be eliminated and vehiclesrsquoreal ldquoshared contribution valuerdquo will be guaranteedWe knowthat in the real network the exaggerated nodes will benefitmore because it means that in the case the other nodes arereal the exaggerated nodes will get more in the next round ofthe game
In VANET based on P2P vehicles provide service for eachother In each stage in the game all the vehicles will broadcasttheir gains So all the vehicles in the network will receive thebroadcast information and accumulate the value accordingto the identity of the vehicles At the end of the stage gameeach vehicle records the stage game information (vehicleidentification total service) of all the vehicles in the networkTherefore the vehicles will refuse to provide service when thenodes choose ldquoexaggeratorrdquo according to their record
In evolutionary game the game of the participants istwo random vehicle nodes Suppose in the whole population
8 International Journal of Distributed Sensor Networks
Table 1 Pay-off matrix
Participant 119894Real Exaggerator
119895
Real 119906(119894) 119906(119895) 119906(119894) + 120572119891 minus119881119895(119905)
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
International Journal of Distributed Sensor Networks 3
efficiently and guarantee service contribution veracityof vehicles in each stage game by evolving of singlepopulation
The target of this paper is to present a RGMPMWincentive mechanism based on the information of servicesevaluation to stimulate vehicles sharing their multimediabased on evolutionary game propose EGV game model toprevent the mendacious service share of vehicles efficientlyand guarantee service contribution veracity of vehicles ineach stage game by evolving of single population in P2P-based VANET
The rest of the paper is organized as follows Relatedwork on evolutionary game and repeated game are presentedin Section 2 Section 3 is system model Section 4 describesfeedback-based REGMPMW incentives scheme Evolution-ary game-based model for veracity of vehicles is reported inSection 5 Section 6 studies the simulation and analysis Weconclude our paper and propose perspectives in Section 7
2 Related Work
Game theory is a mathematical theory and method ofresearching the phenomenon with wrestled or competitiveproperty and under certain restricted conditions the partici-pators can implement strategies to other players tomake surethat the profits of participators reach a final balanced state
21 Evolutionary Game Classical game theory generallyassumes that each individual acts so as to maximize its utilityassuming that the others do the same and understandingcompletely the possible utility payoffs of their interactionsAn alternative perspective from evolutionary game theoryassumes that individuals will copy the behavior of otherswho obtain a higher utility [22] Evolutionary game hastwo core theories evolutionary stable strategy and replicatordynamics equation Evolutionary stable strategy emphasizesthe process of how a dynamic evolution system reaches asteady state and evolutionary stable strategy119909
lowast needs tomeetthe following two conditions first 1199091015840 = Ω(119909
lowast
) = 0 secondΩ1015840
(119909lowast
) lt 06 Replicator dynamic equation describes a
dynamic differential equation on time parameter 119905 taking thenumber of frequency variation Replicator dynamic equationis expressed by 119909
1015840
119894= [120601(119909
119894 119909) minus 120601(119909 119909)]119909
119894 where 119909
119894(119905) is the
proportion of participators who take pure strategy 120601(119909119894 119909) is
the fitness of strategy 119894 and 120601(119909 119909) is the average fitness ofstrategy 119894 [26]
The following describes the standard set of evolutionarygame theory [27]
(1) There is a group of users and the number of the usersin the group is very large
(2) Assuming that pure strategy or action exists Eachmember in the group chooses the strategy from thesame strategy set 119860 = 1 2 119868
(3) Let 119872 = (1199101 119910
119868) | 119910119895
ge 0 sum119868
119895=1119910119895
= 1 bethe possibility distribution set on pure strategy set119868 119872 can be interpreted as a mixed strategy set In
fact assuming that picking the user randomly fromthe group the possibility that the user with markedsign meets the user with strategy 119910 is 119910
119895 After a
few game processes participators who use strategy119895 is equivalent to the face using a mixed strategy ofparticipators
Evolutionary game in network application is very pop-ular and a currently [20ndash25 28] used evolutionary gameto solve the problem of uncooperative two-hop routingmessage forwarding control inDTN (delay tolerant network)Reference [21] used the mathematical framework of gametheory and evolutionary game theory for modeling clearlydemonstrating the connection of cooperation trust privacyand security in a multihop network in order to prevent thefake nodes prevent misuse detect anomalies and to protectusersrsquo privacy Reference [22] studied the resource allocationand the establishment of distribution tree Assuming thatthe allocation of video is based on a multiple descriptionencoder then using evolutionary game can significantlyaffect the scalability fast adaptation twist high degree ofnode cooperation and the autonomous of distributed nodetree network Reference [23] studied an energy manage-ment of stochastic evolutionary game in distributed alohanetwork Each participator may be in different states andcan be involved in the same local interaction during itslifetime Its action decides not only effectiveness but also thetransmission probability and the time of his life Reference[24] analyzed the problem of network dynamic selectionwith evolutionary game in heterogeneous wireless networksIt can guarantee the network performance in the case ofmultipopulation evolutionary game competition References[25] studied the evolutionary game based on the credibilityto forward data safely and deny the service attacks makingsure that the maximum numbers of nodes in the networkforward cooperatively in the autonomous ad hoc and sensornetwork
In P2P-based VANET vehicles move at high speed andinstant contribution is more important therefore in everyrequest slot 119905 each vehicle needs to decide how many mediaservices to share with the request vehicle This decision willaffect its profit in the next stageThus it is reasonable tomodelthe action of vehicles as repeated game
22 Repeated Game Repeated game means the same struc-ture game is repeated for many times where each game iscalled ldquostage gamerdquo Repeated game is an important part ofa dynamic game and it can repeat complete information orincomplete information When the game is executed onlyonce each participator just cares about one-time paymentBut if the game is repeated participators may tend to getlong- term profit instead of immediate profit thereforethey will choose a different equilibrium strategy Thus therepeat number will affect the outcome of equilibrium gameRepeated game has three basic characteristics (a) In therepeated game stage there is no ldquosubstancerdquo connectionbetween games that is to say that the previous stage of thegamewill not change the construction of the next stage (b) Inevery stage of the repeated game all participators can observe
4 International Journal of Distributed Sensor Networks
the history of the game (c) Total profit of participators isthe discounted value sum or weighted average number of allstagesrsquo profit
Repeated game in network application has also beenstudied widely [16 29ndash32] Reference [16] proposed serverdifferentiation incentives for P2P streaming system based onthe immediate profit of nodes At the same time it designeda repeated game model to analyze how much should everynode contribute in every round in this incentive Reference[29] used repeated game theory in FiWi access networkand applied effective quality service routing mechanisms andscheduling policy into practical application Balance strategyguaranteed the quality of service of FiWi wireless networkReference [30] used repeated game model to establish alimited punishment mechanism to enforce selfish nodes tobe unselfish preventing cheating to save energy Reference[31] checked some basic important properties of a rout-ing protocol design The importance of these attributes isautonomous participators from the underlying economicfactorsrsquo management behaviorThe connected price informa-tion in an associated swap is regarded as a repeated gameamong the relevant participators Reference [32] studied themulticast overlay network applications in the framework ofrepeated games and described a repeated gamemodel of userbehaviors to capture the effect of short-term profit to long-term profit
VANET is an autonomous network and participators aregroups or individuals with limited rationality Traditionalgame theory methods assume that participators are entirelyrational Evolutionary game theory is a game addressing nodebounded rationality specifically Therefore it is reasonablethat we use evolutionary game as a research method in thispaper
3 System Model
In VANET there are two main ways of communicationvehicle to vehicle (V2V) and vehicle to RSU (V2R) In theanalysis of part I we only consider V2V communicationunder urban scenes We regard VANET as a network ofvehiclesrsquo set and each vehicle is equipped with communica-tion equipment allowing communication based on 80211pprotocol among different vehicles As is shown in Figure 1nodes begin to download the initial service from RSU thenwhen the vehicle is moving out of the range of RSU servicesIn order to obtain a satisfactory quality of service V2Vcommunication is needed in RSU communication blackoutConsidering a typical P2P-based VANET multimedia ser-vices under urban scenes at a certain time the role of eachvehicle is ldquoRequesterrdquo (ask for service) or ldquoSupplierrdquo (provideservice) As a requester it may face several suppliers withsame services as a supplier it may also face more than onerequester
The ldquoMore Pay for More Work (RGMPMW)rdquo incentivemechanism and EGV game model are used into the urbanVANET with double lane in this paper and the incentive
mechanism performs well The models in the paper areintroduced as follows
31 The Model of Vehicles Encounter VANET is a networkcollection of vehicles 119881 = 1 2 119894 Each vehicle can joinor leave the network at any timeThe running speed of vehicleis V119894 119894 = 1 2 |119881| isin (5 16)ms We use 119889
119894119895isin (1 5000)
to express the distance between vehicle 119894 and vehicle 119895 andthe chance of encounter between vehicles is independentwithno interfering Here we define vehicles that meet within eachtransmission range Assuming the transmission range of theevery vehicle is 250m The probability that vehicle 119894 andvehicle 119895 meet is expressed as 119902
119894119895
119902119894119895
=
V119894minus V119895
005 lowast 119889119894119895
same running direction vehicle 119894 is
behind vehicle 119895 V119894gt V119895
119889119894119895
isin (250 5000)
0 leaving in opposite directionor same runnig directionvehicle 119894 is behind vehicle 119895
V119894lt V119895 119889119894119895
isin (250 5000)
1 move in opposite direction119889119894119895
isin (250 5000) or 119889119894119895
isin (1 250)
(1)
As is shown in Figure 2(a) in the period 119905 minus 1 vehicle 2has the media service which vehicle 1 vehicle 5 and vehicle6 need then they make a service request to vehicle 2 Atthis time node 2 can be regarded as a similar manager ofnodes 1 2 5 and 6 In the next period 119905 there are two vehiclenodes 7 and 8 added into network At this time vehicles5 and 6 run out of the communication range of vehicle 2therefore they make media request from vehicle 7 Vehicle1 and vehicle 2 are running in the same direction so theycan still continue to keep connection At this time vehicle2 loses manage capabilities of vehicles 5 and 6 and vehicle7 becomes the current similar manager of vehicles 5 and 6vehicle 2 becomes the similar manager of vehicles 1 2 4and 8 With the movement of vehicles every vehiclersquos similarmanager is changing in other words the connected timebetween vehicles is not fixed Figure 2 is just a simplifiedmodel only showing a partial service communication In factevery vehicle is a similar manager of a group In this paperwe only consider the situation of one provider and severalrequesters
Because of the mobility of vehicles in VANET it isimpossible to choose a fixed reliable third-party to managea certain number of nodes For simplicity first we assumethat (1) nodes in VANET have their own media services(2) initially each vehicle gets a certain amount of mediaservices from the RSU and gets initialized with a certaincontribution value when entering the network (3) the mediaservice among vehicles is instantaneous and there is no timelimit (4) at the time every vehicle enter the network it is given
International Journal of Distributed Sensor Networks 5
1
2
3
4
5
6
(a) 119905 minus 1
12
3
4
5
6
7
8
(b) 119905
Figure 2 The model of vehicles encounter
a unique real identity (5) the transmission range of vehiclesis the same
32Media ServiceModel In this paper we dividemultimediaservices into four kinds based on the type and popularityof the media (1) critical urgent media services such asroad hazard information and highway information definedas 119875119894(119905) = 09 (2) delay-sensitive services [33] such as
video conference and video service defined as 119875119894(119905) = 07
(3) constantly completed multimedia services like musicentertainment defined as 119875
119894(119905) = 05 (4) life services such
as restaurant hotel information service defined 119875119894(119905) = 02
where 119875119896(119905) represents the popularity of the media provided
by providers in the current stage of the game 119875119896(119905) isin [0 1]
When requesters ask for media service from providerthey will give their shared value of the previous phase to theprovider Since vehicles have a strong ability of computingprovider will determine the allocation of resources based onthe shared value of all requesters Meanwhile at the end ofthe request requesters will broadcast information to all nodesin the network such as information about media serviceprovider and value (Section 4 will describe evaluation ofmedia service in detail) Therefore all nodes in network willstore a list record ID and shared value of all nodes in thenetwork For nodes that just enter the network they will get aunique ID and thenwhen theymeet first node they will copyall records from it to complete information All nodes updaterecords in each time slot
4 Offer-Based RGMPMW Incentives Scheme
Since vehicle nodes in VANET are naturally selfish theywill not go to contribute their resources to other peer nodeswithout motive Therefore we need to design an incentivemechanism to encourage the contribution of nodes [17]
In the P2P-based VANET design of incentivemechanismshould consider instant contribution of vehicles Taking real-time requirement of media streams into account the vehicles
are more strictly required to share their resources in everyround otherwise the requester may not receive the databefore the playback time When implementing incentivemechanism to nodes contribution of current time periodis more important than historical contribution Repeatedgame keeping encouraging nodes to contribute includes alot of repeated game stages of participators In each stagethe decisions of participators all depend on their paymentAn action can be determined by one participator giving itthe highest payment Therefore in the repeated game whenparticipators decide what strategy to take they must careabout current and future payment [29]This paper proposes aRGMPMW incentivemechanism based on similarmanagers
In this incentive mechanism we define a noun ldquosharedcontribution valuerdquo representing the contribution of a nodemade in a game stage It is related to bandwidth popularity ofthemedia and amount of providers of nodesrsquo contribution Inthe sharing mechanism ldquoshared contribution valuerdquo of nodesis evaluated by uploaddownload behavior in a previous stageEach node broadcasts evaluation of servicersquos popularity andimportance before the end of the game In the same stageevery provider is a similar manager and it decides requestersrsquoprofit in current stage based on ldquoshared contribution valuerdquoof previous stage provided by requesters
Therefore the ldquoshared contribution valuerdquo of a node kinstage 119905 is the sum of feedback information provided by allnodes that received the media service of 119896 That is
119881119896(119905) =
119899
sum
119894=1
119862119894(119905) lowast 119875
119894(119905) (2)
For simplicity we assume that the system model in thispaper is that every vehicle node in a slot 119905 provides only onekind of media service Thus the ldquoshared contribution valuerdquoof a node 119896 in slot 119905 can be simplified as
119881119896(119905) = 119862
119896(119905) lowast 119875
119896(119905) (3)
where 119881119896(119905) represents ldquoshared contribution valuerdquo 119862
119896(119905)
represents bandwidth contributed by 119878 and 119875119896(119905) represents
6 International Journal of Distributed Sensor Networks
Figure 3 The model of vehicle requesting
the popularity of the media provided by 119878 in current stage119875119896(119905) isin [0 1]Figure 2 shows the system model of communications
among vehicles under urban scenes in VANET A vehiclemay be both a service provider and a service requester ina stage of the game However in the incentive mechanismproposed in this paper we are most concerned about theldquoshared contribution valuerdquo Here we only consider a simplescenario one provider corresponds to several requesters asis shown in Figure 3
In vehicle request model when a vehicle asks for mediaservices it will give its ldquoshared contribution valuerdquo in previousstage to provider and provider will determine the allocationof resources based on the shared value of all requesters Wedefine the resource assigned from provider 119878 to a requester intime 119905 which is
119866119904119894
(119905) = 119902119894119904
lowast 119866119904lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
(4)
where 119902119894119904
is the meet probability of two vehicles and it isrelated to their the running speed and distance 119866
119904is the
contribution set by provider 119878 in current stage 119881119894(119905 minus 1) is
the ldquoshared contribution valuerdquo of requester 119894 in previousstage 119881
minus119894(119905 minus 1) is the sum ldquoshared contribution valuerdquo of all
requesters except requester 119894Therefore the profit function ofeach node is the difference between the service obtained byprovider and the total service it provides for other requesters
119906119894(119905) = 119866
119904119894(119905) minus 119881
119894(119905) (5)
As vehicle node is autonomous the service media type isdecided by each node In order to obtain greater payoff eachnode tends to choose high popularity of media services We
set119866119904= 119881119904(119905minus1) Then the utility function of requestor 119894 can
be rewritten as
119906119894(119905) = 119902
119894119904lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(6)
In addition we define the total utility of node 119894 in theservice time as follows
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
119906119894(119905) (7)
Here 120575 isin (0 1] is the discount factor and it can beregarded as a nodersquos patience for the subsequent game Thegreater the value is themore patient node is On the contrarythe node will pay more attention to the current earnings Inthe infinite repeated game every participant does not knowwhen the game will end So we assume that the probability ofthe end of the game is 119901
The implementation steps of RGMPMW incentivemechanism based on similar management are shown inAlgorithm 1
We can get from formulas (6) and (7) the following
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast 119902119894119904
lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(8)
The goal of the node 119894 is to maximize 119906(119894) First we canget the formula (9) by a series of deformation for the formula(7)
119906 (119894) =
119881119904(0)
119881119894(0) + 119881
minus119894(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119894(119905)
119881119894(119905) + 119881
minus119894(119905)
minus 119881119894(119905)
(9)
where 119881119896(0) is the initialization ldquoshared contribution valuerdquo
when the node 119896 comes into the network at the beginning So119881119904(0)(119881
119894(0) + 119881
minus119894(0)) is a constant After deformation each
item is independent in the sum Therefore we can make thesum maximized by maximizing each item
We set119889 ([120575 (1 minus 119901)] lowast 119902
where 119899 is the number of vehicles requesting node 119878Putting the formula (14) to the formula (12) we can get
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
1198992
=
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904
(15)
The payoff of the node will be maximized when theequation above equation is established
5 Evolutionary Game Model forVeracity of Vehicles
In Section 4 the function of RGMPMW incentives schemebased on information is when the node is rational it willactively share its media resource to gain more payoffs But inVANETwhich is autonomic network it is not practical for thenode to be completely rational In the process of each gameif each requestorrsquos ldquoshared contribution valuerdquo is stable atpresent namely node ldquoshared contribution valuerdquo fluctuation
is small he will get unexpected payoff when one requesterexaggerates his previous contribution or there are attacksof malicious nodes which exaggerate their contributiondeliberately and make the payoffs low So we should studynode bounded rationality in VANET and the situation thatthe nodes do not trust each other In this section we presentan EGV game model by using a game theory which can beapplied to the node bounded rationality which can preventthe node exaggerating its ldquoshared contribution valuerdquo togain extra payoff or malicious attacks and to guarantee theauthenticity of all the nodes
51 Structure and Solution of Evolutionary Game In thispaper we set the vehicles which request for the same vehicleas an evolutionary group Researching on evolutionary gametheory amutation of disadvantage group is the vehicleswhichexaggerate their own shared services for more payoffs andreduce the payoff of the other competitors After a longevolution disadvantage groupwill be eliminated and vehiclesrsquoreal ldquoshared contribution valuerdquo will be guaranteedWe knowthat in the real network the exaggerated nodes will benefitmore because it means that in the case the other nodes arereal the exaggerated nodes will get more in the next round ofthe game
In VANET based on P2P vehicles provide service for eachother In each stage in the game all the vehicles will broadcasttheir gains So all the vehicles in the network will receive thebroadcast information and accumulate the value accordingto the identity of the vehicles At the end of the stage gameeach vehicle records the stage game information (vehicleidentification total service) of all the vehicles in the networkTherefore the vehicles will refuse to provide service when thenodes choose ldquoexaggeratorrdquo according to their record
In evolutionary game the game of the participants istwo random vehicle nodes Suppose in the whole population
8 International Journal of Distributed Sensor Networks
Table 1 Pay-off matrix
Participant 119894Real Exaggerator
119895
Real 119906(119894) 119906(119895) 119906(119894) + 120572119891 minus119881119895(119905)
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
4 International Journal of Distributed Sensor Networks
the history of the game (c) Total profit of participators isthe discounted value sum or weighted average number of allstagesrsquo profit
Repeated game in network application has also beenstudied widely [16 29ndash32] Reference [16] proposed serverdifferentiation incentives for P2P streaming system based onthe immediate profit of nodes At the same time it designeda repeated game model to analyze how much should everynode contribute in every round in this incentive Reference[29] used repeated game theory in FiWi access networkand applied effective quality service routing mechanisms andscheduling policy into practical application Balance strategyguaranteed the quality of service of FiWi wireless networkReference [30] used repeated game model to establish alimited punishment mechanism to enforce selfish nodes tobe unselfish preventing cheating to save energy Reference[31] checked some basic important properties of a rout-ing protocol design The importance of these attributes isautonomous participators from the underlying economicfactorsrsquo management behaviorThe connected price informa-tion in an associated swap is regarded as a repeated gameamong the relevant participators Reference [32] studied themulticast overlay network applications in the framework ofrepeated games and described a repeated gamemodel of userbehaviors to capture the effect of short-term profit to long-term profit
VANET is an autonomous network and participators aregroups or individuals with limited rationality Traditionalgame theory methods assume that participators are entirelyrational Evolutionary game theory is a game addressing nodebounded rationality specifically Therefore it is reasonablethat we use evolutionary game as a research method in thispaper
3 System Model
In VANET there are two main ways of communicationvehicle to vehicle (V2V) and vehicle to RSU (V2R) In theanalysis of part I we only consider V2V communicationunder urban scenes We regard VANET as a network ofvehiclesrsquo set and each vehicle is equipped with communica-tion equipment allowing communication based on 80211pprotocol among different vehicles As is shown in Figure 1nodes begin to download the initial service from RSU thenwhen the vehicle is moving out of the range of RSU servicesIn order to obtain a satisfactory quality of service V2Vcommunication is needed in RSU communication blackoutConsidering a typical P2P-based VANET multimedia ser-vices under urban scenes at a certain time the role of eachvehicle is ldquoRequesterrdquo (ask for service) or ldquoSupplierrdquo (provideservice) As a requester it may face several suppliers withsame services as a supplier it may also face more than onerequester
The ldquoMore Pay for More Work (RGMPMW)rdquo incentivemechanism and EGV game model are used into the urbanVANET with double lane in this paper and the incentive
mechanism performs well The models in the paper areintroduced as follows
31 The Model of Vehicles Encounter VANET is a networkcollection of vehicles 119881 = 1 2 119894 Each vehicle can joinor leave the network at any timeThe running speed of vehicleis V119894 119894 = 1 2 |119881| isin (5 16)ms We use 119889
119894119895isin (1 5000)
to express the distance between vehicle 119894 and vehicle 119895 andthe chance of encounter between vehicles is independentwithno interfering Here we define vehicles that meet within eachtransmission range Assuming the transmission range of theevery vehicle is 250m The probability that vehicle 119894 andvehicle 119895 meet is expressed as 119902
119894119895
119902119894119895
=
V119894minus V119895
005 lowast 119889119894119895
same running direction vehicle 119894 is
behind vehicle 119895 V119894gt V119895
119889119894119895
isin (250 5000)
0 leaving in opposite directionor same runnig directionvehicle 119894 is behind vehicle 119895
V119894lt V119895 119889119894119895
isin (250 5000)
1 move in opposite direction119889119894119895
isin (250 5000) or 119889119894119895
isin (1 250)
(1)
As is shown in Figure 2(a) in the period 119905 minus 1 vehicle 2has the media service which vehicle 1 vehicle 5 and vehicle6 need then they make a service request to vehicle 2 Atthis time node 2 can be regarded as a similar manager ofnodes 1 2 5 and 6 In the next period 119905 there are two vehiclenodes 7 and 8 added into network At this time vehicles5 and 6 run out of the communication range of vehicle 2therefore they make media request from vehicle 7 Vehicle1 and vehicle 2 are running in the same direction so theycan still continue to keep connection At this time vehicle2 loses manage capabilities of vehicles 5 and 6 and vehicle7 becomes the current similar manager of vehicles 5 and 6vehicle 2 becomes the similar manager of vehicles 1 2 4and 8 With the movement of vehicles every vehiclersquos similarmanager is changing in other words the connected timebetween vehicles is not fixed Figure 2 is just a simplifiedmodel only showing a partial service communication In factevery vehicle is a similar manager of a group In this paperwe only consider the situation of one provider and severalrequesters
Because of the mobility of vehicles in VANET it isimpossible to choose a fixed reliable third-party to managea certain number of nodes For simplicity first we assumethat (1) nodes in VANET have their own media services(2) initially each vehicle gets a certain amount of mediaservices from the RSU and gets initialized with a certaincontribution value when entering the network (3) the mediaservice among vehicles is instantaneous and there is no timelimit (4) at the time every vehicle enter the network it is given
International Journal of Distributed Sensor Networks 5
1
2
3
4
5
6
(a) 119905 minus 1
12
3
4
5
6
7
8
(b) 119905
Figure 2 The model of vehicles encounter
a unique real identity (5) the transmission range of vehiclesis the same
32Media ServiceModel In this paper we dividemultimediaservices into four kinds based on the type and popularityof the media (1) critical urgent media services such asroad hazard information and highway information definedas 119875119894(119905) = 09 (2) delay-sensitive services [33] such as
video conference and video service defined as 119875119894(119905) = 07
(3) constantly completed multimedia services like musicentertainment defined as 119875
119894(119905) = 05 (4) life services such
as restaurant hotel information service defined 119875119894(119905) = 02
where 119875119896(119905) represents the popularity of the media provided
by providers in the current stage of the game 119875119896(119905) isin [0 1]
When requesters ask for media service from providerthey will give their shared value of the previous phase to theprovider Since vehicles have a strong ability of computingprovider will determine the allocation of resources based onthe shared value of all requesters Meanwhile at the end ofthe request requesters will broadcast information to all nodesin the network such as information about media serviceprovider and value (Section 4 will describe evaluation ofmedia service in detail) Therefore all nodes in network willstore a list record ID and shared value of all nodes in thenetwork For nodes that just enter the network they will get aunique ID and thenwhen theymeet first node they will copyall records from it to complete information All nodes updaterecords in each time slot
4 Offer-Based RGMPMW Incentives Scheme
Since vehicle nodes in VANET are naturally selfish theywill not go to contribute their resources to other peer nodeswithout motive Therefore we need to design an incentivemechanism to encourage the contribution of nodes [17]
In the P2P-based VANET design of incentivemechanismshould consider instant contribution of vehicles Taking real-time requirement of media streams into account the vehicles
are more strictly required to share their resources in everyround otherwise the requester may not receive the databefore the playback time When implementing incentivemechanism to nodes contribution of current time periodis more important than historical contribution Repeatedgame keeping encouraging nodes to contribute includes alot of repeated game stages of participators In each stagethe decisions of participators all depend on their paymentAn action can be determined by one participator giving itthe highest payment Therefore in the repeated game whenparticipators decide what strategy to take they must careabout current and future payment [29]This paper proposes aRGMPMW incentivemechanism based on similarmanagers
In this incentive mechanism we define a noun ldquosharedcontribution valuerdquo representing the contribution of a nodemade in a game stage It is related to bandwidth popularity ofthemedia and amount of providers of nodesrsquo contribution Inthe sharing mechanism ldquoshared contribution valuerdquo of nodesis evaluated by uploaddownload behavior in a previous stageEach node broadcasts evaluation of servicersquos popularity andimportance before the end of the game In the same stageevery provider is a similar manager and it decides requestersrsquoprofit in current stage based on ldquoshared contribution valuerdquoof previous stage provided by requesters
Therefore the ldquoshared contribution valuerdquo of a node kinstage 119905 is the sum of feedback information provided by allnodes that received the media service of 119896 That is
119881119896(119905) =
119899
sum
119894=1
119862119894(119905) lowast 119875
119894(119905) (2)
For simplicity we assume that the system model in thispaper is that every vehicle node in a slot 119905 provides only onekind of media service Thus the ldquoshared contribution valuerdquoof a node 119896 in slot 119905 can be simplified as
119881119896(119905) = 119862
119896(119905) lowast 119875
119896(119905) (3)
where 119881119896(119905) represents ldquoshared contribution valuerdquo 119862
119896(119905)
represents bandwidth contributed by 119878 and 119875119896(119905) represents
6 International Journal of Distributed Sensor Networks
Figure 3 The model of vehicle requesting
the popularity of the media provided by 119878 in current stage119875119896(119905) isin [0 1]Figure 2 shows the system model of communications
among vehicles under urban scenes in VANET A vehiclemay be both a service provider and a service requester ina stage of the game However in the incentive mechanismproposed in this paper we are most concerned about theldquoshared contribution valuerdquo Here we only consider a simplescenario one provider corresponds to several requesters asis shown in Figure 3
In vehicle request model when a vehicle asks for mediaservices it will give its ldquoshared contribution valuerdquo in previousstage to provider and provider will determine the allocationof resources based on the shared value of all requesters Wedefine the resource assigned from provider 119878 to a requester intime 119905 which is
119866119904119894
(119905) = 119902119894119904
lowast 119866119904lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
(4)
where 119902119894119904
is the meet probability of two vehicles and it isrelated to their the running speed and distance 119866
119904is the
contribution set by provider 119878 in current stage 119881119894(119905 minus 1) is
the ldquoshared contribution valuerdquo of requester 119894 in previousstage 119881
minus119894(119905 minus 1) is the sum ldquoshared contribution valuerdquo of all
requesters except requester 119894Therefore the profit function ofeach node is the difference between the service obtained byprovider and the total service it provides for other requesters
119906119894(119905) = 119866
119904119894(119905) minus 119881
119894(119905) (5)
As vehicle node is autonomous the service media type isdecided by each node In order to obtain greater payoff eachnode tends to choose high popularity of media services We
set119866119904= 119881119904(119905minus1) Then the utility function of requestor 119894 can
be rewritten as
119906119894(119905) = 119902
119894119904lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(6)
In addition we define the total utility of node 119894 in theservice time as follows
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
119906119894(119905) (7)
Here 120575 isin (0 1] is the discount factor and it can beregarded as a nodersquos patience for the subsequent game Thegreater the value is themore patient node is On the contrarythe node will pay more attention to the current earnings Inthe infinite repeated game every participant does not knowwhen the game will end So we assume that the probability ofthe end of the game is 119901
The implementation steps of RGMPMW incentivemechanism based on similar management are shown inAlgorithm 1
We can get from formulas (6) and (7) the following
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast 119902119894119904
lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(8)
The goal of the node 119894 is to maximize 119906(119894) First we canget the formula (9) by a series of deformation for the formula(7)
119906 (119894) =
119881119904(0)
119881119894(0) + 119881
minus119894(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119894(119905)
119881119894(119905) + 119881
minus119894(119905)
minus 119881119894(119905)
(9)
where 119881119896(0) is the initialization ldquoshared contribution valuerdquo
when the node 119896 comes into the network at the beginning So119881119904(0)(119881
119894(0) + 119881
minus119894(0)) is a constant After deformation each
item is independent in the sum Therefore we can make thesum maximized by maximizing each item
We set119889 ([120575 (1 minus 119901)] lowast 119902
where 119899 is the number of vehicles requesting node 119878Putting the formula (14) to the formula (12) we can get
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
1198992
=
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904
(15)
The payoff of the node will be maximized when theequation above equation is established
5 Evolutionary Game Model forVeracity of Vehicles
In Section 4 the function of RGMPMW incentives schemebased on information is when the node is rational it willactively share its media resource to gain more payoffs But inVANETwhich is autonomic network it is not practical for thenode to be completely rational In the process of each gameif each requestorrsquos ldquoshared contribution valuerdquo is stable atpresent namely node ldquoshared contribution valuerdquo fluctuation
is small he will get unexpected payoff when one requesterexaggerates his previous contribution or there are attacksof malicious nodes which exaggerate their contributiondeliberately and make the payoffs low So we should studynode bounded rationality in VANET and the situation thatthe nodes do not trust each other In this section we presentan EGV game model by using a game theory which can beapplied to the node bounded rationality which can preventthe node exaggerating its ldquoshared contribution valuerdquo togain extra payoff or malicious attacks and to guarantee theauthenticity of all the nodes
51 Structure and Solution of Evolutionary Game In thispaper we set the vehicles which request for the same vehicleas an evolutionary group Researching on evolutionary gametheory amutation of disadvantage group is the vehicleswhichexaggerate their own shared services for more payoffs andreduce the payoff of the other competitors After a longevolution disadvantage groupwill be eliminated and vehiclesrsquoreal ldquoshared contribution valuerdquo will be guaranteedWe knowthat in the real network the exaggerated nodes will benefitmore because it means that in the case the other nodes arereal the exaggerated nodes will get more in the next round ofthe game
In VANET based on P2P vehicles provide service for eachother In each stage in the game all the vehicles will broadcasttheir gains So all the vehicles in the network will receive thebroadcast information and accumulate the value accordingto the identity of the vehicles At the end of the stage gameeach vehicle records the stage game information (vehicleidentification total service) of all the vehicles in the networkTherefore the vehicles will refuse to provide service when thenodes choose ldquoexaggeratorrdquo according to their record
In evolutionary game the game of the participants istwo random vehicle nodes Suppose in the whole population
8 International Journal of Distributed Sensor Networks
Table 1 Pay-off matrix
Participant 119894Real Exaggerator
119895
Real 119906(119894) 119906(119895) 119906(119894) + 120572119891 minus119881119895(119905)
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
International Journal of Distributed Sensor Networks 5
1
2
3
4
5
6
(a) 119905 minus 1
12
3
4
5
6
7
8
(b) 119905
Figure 2 The model of vehicles encounter
a unique real identity (5) the transmission range of vehiclesis the same
32Media ServiceModel In this paper we dividemultimediaservices into four kinds based on the type and popularityof the media (1) critical urgent media services such asroad hazard information and highway information definedas 119875119894(119905) = 09 (2) delay-sensitive services [33] such as
video conference and video service defined as 119875119894(119905) = 07
(3) constantly completed multimedia services like musicentertainment defined as 119875
119894(119905) = 05 (4) life services such
as restaurant hotel information service defined 119875119894(119905) = 02
where 119875119896(119905) represents the popularity of the media provided
by providers in the current stage of the game 119875119896(119905) isin [0 1]
When requesters ask for media service from providerthey will give their shared value of the previous phase to theprovider Since vehicles have a strong ability of computingprovider will determine the allocation of resources based onthe shared value of all requesters Meanwhile at the end ofthe request requesters will broadcast information to all nodesin the network such as information about media serviceprovider and value (Section 4 will describe evaluation ofmedia service in detail) Therefore all nodes in network willstore a list record ID and shared value of all nodes in thenetwork For nodes that just enter the network they will get aunique ID and thenwhen theymeet first node they will copyall records from it to complete information All nodes updaterecords in each time slot
4 Offer-Based RGMPMW Incentives Scheme
Since vehicle nodes in VANET are naturally selfish theywill not go to contribute their resources to other peer nodeswithout motive Therefore we need to design an incentivemechanism to encourage the contribution of nodes [17]
In the P2P-based VANET design of incentivemechanismshould consider instant contribution of vehicles Taking real-time requirement of media streams into account the vehicles
are more strictly required to share their resources in everyround otherwise the requester may not receive the databefore the playback time When implementing incentivemechanism to nodes contribution of current time periodis more important than historical contribution Repeatedgame keeping encouraging nodes to contribute includes alot of repeated game stages of participators In each stagethe decisions of participators all depend on their paymentAn action can be determined by one participator giving itthe highest payment Therefore in the repeated game whenparticipators decide what strategy to take they must careabout current and future payment [29]This paper proposes aRGMPMW incentivemechanism based on similarmanagers
In this incentive mechanism we define a noun ldquosharedcontribution valuerdquo representing the contribution of a nodemade in a game stage It is related to bandwidth popularity ofthemedia and amount of providers of nodesrsquo contribution Inthe sharing mechanism ldquoshared contribution valuerdquo of nodesis evaluated by uploaddownload behavior in a previous stageEach node broadcasts evaluation of servicersquos popularity andimportance before the end of the game In the same stageevery provider is a similar manager and it decides requestersrsquoprofit in current stage based on ldquoshared contribution valuerdquoof previous stage provided by requesters
Therefore the ldquoshared contribution valuerdquo of a node kinstage 119905 is the sum of feedback information provided by allnodes that received the media service of 119896 That is
119881119896(119905) =
119899
sum
119894=1
119862119894(119905) lowast 119875
119894(119905) (2)
For simplicity we assume that the system model in thispaper is that every vehicle node in a slot 119905 provides only onekind of media service Thus the ldquoshared contribution valuerdquoof a node 119896 in slot 119905 can be simplified as
119881119896(119905) = 119862
119896(119905) lowast 119875
119896(119905) (3)
where 119881119896(119905) represents ldquoshared contribution valuerdquo 119862
119896(119905)
represents bandwidth contributed by 119878 and 119875119896(119905) represents
6 International Journal of Distributed Sensor Networks
Figure 3 The model of vehicle requesting
the popularity of the media provided by 119878 in current stage119875119896(119905) isin [0 1]Figure 2 shows the system model of communications
among vehicles under urban scenes in VANET A vehiclemay be both a service provider and a service requester ina stage of the game However in the incentive mechanismproposed in this paper we are most concerned about theldquoshared contribution valuerdquo Here we only consider a simplescenario one provider corresponds to several requesters asis shown in Figure 3
In vehicle request model when a vehicle asks for mediaservices it will give its ldquoshared contribution valuerdquo in previousstage to provider and provider will determine the allocationof resources based on the shared value of all requesters Wedefine the resource assigned from provider 119878 to a requester intime 119905 which is
119866119904119894
(119905) = 119902119894119904
lowast 119866119904lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
(4)
where 119902119894119904
is the meet probability of two vehicles and it isrelated to their the running speed and distance 119866
119904is the
contribution set by provider 119878 in current stage 119881119894(119905 minus 1) is
the ldquoshared contribution valuerdquo of requester 119894 in previousstage 119881
minus119894(119905 minus 1) is the sum ldquoshared contribution valuerdquo of all
requesters except requester 119894Therefore the profit function ofeach node is the difference between the service obtained byprovider and the total service it provides for other requesters
119906119894(119905) = 119866
119904119894(119905) minus 119881
119894(119905) (5)
As vehicle node is autonomous the service media type isdecided by each node In order to obtain greater payoff eachnode tends to choose high popularity of media services We
set119866119904= 119881119904(119905minus1) Then the utility function of requestor 119894 can
be rewritten as
119906119894(119905) = 119902
119894119904lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(6)
In addition we define the total utility of node 119894 in theservice time as follows
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
119906119894(119905) (7)
Here 120575 isin (0 1] is the discount factor and it can beregarded as a nodersquos patience for the subsequent game Thegreater the value is themore patient node is On the contrarythe node will pay more attention to the current earnings Inthe infinite repeated game every participant does not knowwhen the game will end So we assume that the probability ofthe end of the game is 119901
The implementation steps of RGMPMW incentivemechanism based on similar management are shown inAlgorithm 1
We can get from formulas (6) and (7) the following
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast 119902119894119904
lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(8)
The goal of the node 119894 is to maximize 119906(119894) First we canget the formula (9) by a series of deformation for the formula(7)
119906 (119894) =
119881119904(0)
119881119894(0) + 119881
minus119894(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119894(119905)
119881119894(119905) + 119881
minus119894(119905)
minus 119881119894(119905)
(9)
where 119881119896(0) is the initialization ldquoshared contribution valuerdquo
when the node 119896 comes into the network at the beginning So119881119904(0)(119881
119894(0) + 119881
minus119894(0)) is a constant After deformation each
item is independent in the sum Therefore we can make thesum maximized by maximizing each item
We set119889 ([120575 (1 minus 119901)] lowast 119902
where 119899 is the number of vehicles requesting node 119878Putting the formula (14) to the formula (12) we can get
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
1198992
=
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904
(15)
The payoff of the node will be maximized when theequation above equation is established
5 Evolutionary Game Model forVeracity of Vehicles
In Section 4 the function of RGMPMW incentives schemebased on information is when the node is rational it willactively share its media resource to gain more payoffs But inVANETwhich is autonomic network it is not practical for thenode to be completely rational In the process of each gameif each requestorrsquos ldquoshared contribution valuerdquo is stable atpresent namely node ldquoshared contribution valuerdquo fluctuation
is small he will get unexpected payoff when one requesterexaggerates his previous contribution or there are attacksof malicious nodes which exaggerate their contributiondeliberately and make the payoffs low So we should studynode bounded rationality in VANET and the situation thatthe nodes do not trust each other In this section we presentan EGV game model by using a game theory which can beapplied to the node bounded rationality which can preventthe node exaggerating its ldquoshared contribution valuerdquo togain extra payoff or malicious attacks and to guarantee theauthenticity of all the nodes
51 Structure and Solution of Evolutionary Game In thispaper we set the vehicles which request for the same vehicleas an evolutionary group Researching on evolutionary gametheory amutation of disadvantage group is the vehicleswhichexaggerate their own shared services for more payoffs andreduce the payoff of the other competitors After a longevolution disadvantage groupwill be eliminated and vehiclesrsquoreal ldquoshared contribution valuerdquo will be guaranteedWe knowthat in the real network the exaggerated nodes will benefitmore because it means that in the case the other nodes arereal the exaggerated nodes will get more in the next round ofthe game
In VANET based on P2P vehicles provide service for eachother In each stage in the game all the vehicles will broadcasttheir gains So all the vehicles in the network will receive thebroadcast information and accumulate the value accordingto the identity of the vehicles At the end of the stage gameeach vehicle records the stage game information (vehicleidentification total service) of all the vehicles in the networkTherefore the vehicles will refuse to provide service when thenodes choose ldquoexaggeratorrdquo according to their record
In evolutionary game the game of the participants istwo random vehicle nodes Suppose in the whole population
8 International Journal of Distributed Sensor Networks
Table 1 Pay-off matrix
Participant 119894Real Exaggerator
119895
Real 119906(119894) 119906(119895) 119906(119894) + 120572119891 minus119881119895(119905)
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
6 International Journal of Distributed Sensor Networks
Figure 3 The model of vehicle requesting
the popularity of the media provided by 119878 in current stage119875119896(119905) isin [0 1]Figure 2 shows the system model of communications
among vehicles under urban scenes in VANET A vehiclemay be both a service provider and a service requester ina stage of the game However in the incentive mechanismproposed in this paper we are most concerned about theldquoshared contribution valuerdquo Here we only consider a simplescenario one provider corresponds to several requesters asis shown in Figure 3
In vehicle request model when a vehicle asks for mediaservices it will give its ldquoshared contribution valuerdquo in previousstage to provider and provider will determine the allocationof resources based on the shared value of all requesters Wedefine the resource assigned from provider 119878 to a requester intime 119905 which is
119866119904119894
(119905) = 119902119894119904
lowast 119866119904lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
(4)
where 119902119894119904
is the meet probability of two vehicles and it isrelated to their the running speed and distance 119866
119904is the
contribution set by provider 119878 in current stage 119881119894(119905 minus 1) is
the ldquoshared contribution valuerdquo of requester 119894 in previousstage 119881
minus119894(119905 minus 1) is the sum ldquoshared contribution valuerdquo of all
requesters except requester 119894Therefore the profit function ofeach node is the difference between the service obtained byprovider and the total service it provides for other requesters
119906119894(119905) = 119866
119904119894(119905) minus 119881
119894(119905) (5)
As vehicle node is autonomous the service media type isdecided by each node In order to obtain greater payoff eachnode tends to choose high popularity of media services We
set119866119904= 119881119904(119905minus1) Then the utility function of requestor 119894 can
be rewritten as
119906119894(119905) = 119902
119894119904lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(6)
In addition we define the total utility of node 119894 in theservice time as follows
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
119906119894(119905) (7)
Here 120575 isin (0 1] is the discount factor and it can beregarded as a nodersquos patience for the subsequent game Thegreater the value is themore patient node is On the contrarythe node will pay more attention to the current earnings Inthe infinite repeated game every participant does not knowwhen the game will end So we assume that the probability ofthe end of the game is 119901
The implementation steps of RGMPMW incentivemechanism based on similar management are shown inAlgorithm 1
We can get from formulas (6) and (7) the following
119906 (119894) =
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast 119902119894119904
lowast 119881119904(119905 minus 1) lowast
119881119894(119905 minus 1)
119881119894(119905 minus 1) + 119881
minus119894(119905 minus 1)
minus 119881119894(119905)
(8)
The goal of the node 119894 is to maximize 119906(119894) First we canget the formula (9) by a series of deformation for the formula(7)
119906 (119894) =
119881119904(0)
119881119894(0) + 119881
minus119894(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119894(119905)
119881119894(119905) + 119881
minus119894(119905)
minus 119881119894(119905)
(9)
where 119881119896(0) is the initialization ldquoshared contribution valuerdquo
when the node 119896 comes into the network at the beginning So119881119904(0)(119881
119894(0) + 119881
minus119894(0)) is a constant After deformation each
item is independent in the sum Therefore we can make thesum maximized by maximizing each item
We set119889 ([120575 (1 minus 119901)] lowast 119902
where 119899 is the number of vehicles requesting node 119878Putting the formula (14) to the formula (12) we can get
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
1198992
=
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904
(15)
The payoff of the node will be maximized when theequation above equation is established
5 Evolutionary Game Model forVeracity of Vehicles
In Section 4 the function of RGMPMW incentives schemebased on information is when the node is rational it willactively share its media resource to gain more payoffs But inVANETwhich is autonomic network it is not practical for thenode to be completely rational In the process of each gameif each requestorrsquos ldquoshared contribution valuerdquo is stable atpresent namely node ldquoshared contribution valuerdquo fluctuation
is small he will get unexpected payoff when one requesterexaggerates his previous contribution or there are attacksof malicious nodes which exaggerate their contributiondeliberately and make the payoffs low So we should studynode bounded rationality in VANET and the situation thatthe nodes do not trust each other In this section we presentan EGV game model by using a game theory which can beapplied to the node bounded rationality which can preventthe node exaggerating its ldquoshared contribution valuerdquo togain extra payoff or malicious attacks and to guarantee theauthenticity of all the nodes
51 Structure and Solution of Evolutionary Game In thispaper we set the vehicles which request for the same vehicleas an evolutionary group Researching on evolutionary gametheory amutation of disadvantage group is the vehicleswhichexaggerate their own shared services for more payoffs andreduce the payoff of the other competitors After a longevolution disadvantage groupwill be eliminated and vehiclesrsquoreal ldquoshared contribution valuerdquo will be guaranteedWe knowthat in the real network the exaggerated nodes will benefitmore because it means that in the case the other nodes arereal the exaggerated nodes will get more in the next round ofthe game
In VANET based on P2P vehicles provide service for eachother In each stage in the game all the vehicles will broadcasttheir gains So all the vehicles in the network will receive thebroadcast information and accumulate the value accordingto the identity of the vehicles At the end of the stage gameeach vehicle records the stage game information (vehicleidentification total service) of all the vehicles in the networkTherefore the vehicles will refuse to provide service when thenodes choose ldquoexaggeratorrdquo according to their record
In evolutionary game the game of the participants istwo random vehicle nodes Suppose in the whole population
8 International Journal of Distributed Sensor Networks
Table 1 Pay-off matrix
Participant 119894Real Exaggerator
119895
Real 119906(119894) 119906(119895) 119906(119894) + 120572119891 minus119881119895(119905)
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
where 119899 is the number of vehicles requesting node 119878Putting the formula (14) to the formula (12) we can get
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
1198992
=
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904
(15)
The payoff of the node will be maximized when theequation above equation is established
5 Evolutionary Game Model forVeracity of Vehicles
In Section 4 the function of RGMPMW incentives schemebased on information is when the node is rational it willactively share its media resource to gain more payoffs But inVANETwhich is autonomic network it is not practical for thenode to be completely rational In the process of each gameif each requestorrsquos ldquoshared contribution valuerdquo is stable atpresent namely node ldquoshared contribution valuerdquo fluctuation
is small he will get unexpected payoff when one requesterexaggerates his previous contribution or there are attacksof malicious nodes which exaggerate their contributiondeliberately and make the payoffs low So we should studynode bounded rationality in VANET and the situation thatthe nodes do not trust each other In this section we presentan EGV game model by using a game theory which can beapplied to the node bounded rationality which can preventthe node exaggerating its ldquoshared contribution valuerdquo togain extra payoff or malicious attacks and to guarantee theauthenticity of all the nodes
51 Structure and Solution of Evolutionary Game In thispaper we set the vehicles which request for the same vehicleas an evolutionary group Researching on evolutionary gametheory amutation of disadvantage group is the vehicleswhichexaggerate their own shared services for more payoffs andreduce the payoff of the other competitors After a longevolution disadvantage groupwill be eliminated and vehiclesrsquoreal ldquoshared contribution valuerdquo will be guaranteedWe knowthat in the real network the exaggerated nodes will benefitmore because it means that in the case the other nodes arereal the exaggerated nodes will get more in the next round ofthe game
In VANET based on P2P vehicles provide service for eachother In each stage in the game all the vehicles will broadcasttheir gains So all the vehicles in the network will receive thebroadcast information and accumulate the value accordingto the identity of the vehicles At the end of the stage gameeach vehicle records the stage game information (vehicleidentification total service) of all the vehicles in the networkTherefore the vehicles will refuse to provide service when thenodes choose ldquoexaggeratorrdquo according to their record
In evolutionary game the game of the participants istwo random vehicle nodes Suppose in the whole population
8 International Journal of Distributed Sensor Networks
Table 1 Pay-off matrix
Participant 119894Real Exaggerator
119895
Real 119906(119894) 119906(119895) 119906(119894) + 120572119891 minus119881119895(119905)
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
that the population strategy set is real exaggerated If thetwo participants 119868 and 119895 are both real their payoffs are 119906(119894)
and 119906(119895) if participants exaggerate their services it will bepunished and the provider refuses to provide them servicesthe real party will get the rewards 120572119891 where 119891 is the rewardunit and 120572 is the strength of the rewardTherefore the pay-offmatrix is as in Table 1
We define that 1205740(119905) is the number of nodes choosing the
ldquorealrdquo strategy and 1205741(119905) is the number of nodes choosing the
ldquoexaggeratorrdquo strategy Their relation is
120574 (119905) = 1205740(119905) + 120574
1(119905) (16)
We set 119909(119905) = 1205740(119905)120574(119905) on behalf of the proportion of the
peer following the strategy ldquorealrdquo then proportion of the peerfollowing the strategy ldquoexaggeraterdquo is 1 minus 119909(119905)
According to the game matrix the payoff of game partieschoosing the real strategy is
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891
(17)
The payoff of choosing exaggerated strategy is
119880119873119881
119896= minus119881119896(119905) (18)
The average payoff is
119880119860
119896= 119909 (119905) lowast 119880
119881
119896+ [1 minus 119909 (119905)] 119880
119873119881
119896
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 119909 (119905) minus 119881119896(119905) [1 minus 119909 (119905)]
(19)
The replication dynamic below indicates how evolutionmakes dynamic change in particular it can be converted tothe equilibrium dynamically by replication dynamic Repli-cator dynamic describes a population evolution process withmultiple strategies Each individual in the population obeysthe following imitation rules after studying the individualchoose the strategy getting more benefit
We assume that each stage game begins from 119896119905 119896 isin 119873and ends at (119896 + 1)119905 119896 isin 119873 The average payoff of the node isrelated to game rivals Suppose in a very small time interval120576 that only the 120576 part participates in the game So in time119905 + 120576 the nodesrsquo average payoff for adopting strategy 119894 can beexpressed as [20]
120574119894(119905 + 120576) = (1 minus 120576) 120574
minus [119906 (119896) + [1 minus 119909 (119905)] 120572119891] 119909 (119905)
+119881119896(119905) [1 minus 119909 (119905)]
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)]
(25)
We set 119865(119909) = 119889119909119889119905 so
119865 (119909) =
119909 (119905 + 1) minus 119909 (119905)
Δ119905
= 119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) (119909 (119905) minus 119909
2
(119905))
(26)
According to the first condition ESS (evolutionary stablestrategy) meeting we make 119889119909119889119905 = 0 that is
119906 (119896) + [1 minus 119909 (119905)] 120572119891 + 119881119896(119905) [119909 (119905) minus 119909
2
(119905)] = 0 (27)
The solution is 1199091(119905) = (119906(119896) + 119881
119896(119905))120572119891 + 1 119909
2(119905) = 0
1199093(119905) = 1
52 Stability Analysis The above three conditions of solu-tions are not all ESS We need according to the secondcondition ESS meeting to analyze the stability
Theorem 1 In EGV gamemodel there is only an evolutionarystable strategy of ESS
Proof According to the second condition ESS meeting weknow that in the ESS 119865(119909) meet the conditions are
119865 (119909lowast
) = 0
1198651015840
(119909lowast
) lt 0
(28)
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
International Journal of Distributed Sensor Networks 9
Therefore we have the analysis as follows
(1) According to the introduction of RGMPMW incen-tive mechanism in Section 4 119906(119896) gt 0 119881
119896(119905) gt 0
because it is the reward of real participants (119906(119896) +
119881119896(119905))120572119891 gt 0 And because 119909 is the ratio of choosing
real that is 119909(119905) isin [0 1] 119909(119905) cannot equal to (119906(119896) +
119881119896(119905))120572119891 + 1
(2) Next we analyze the case when 1199092
= 0 1199093
= 1According to the analysis of (1) we can get 119906(119896) +
(1 minus 119909)120572119891 +119881119896(119905) gt 0 Therefore replication dynamic
evolution graph is as in Figure 11
Assuming that there are 120578 proportion of players inthe game deviating from the strategy ldquorealrdquo and select theldquoexaggeratedrdquo there are
Therefore 119909(119905)3= 1 is the evolution stable strategy ESS
Assuming that there are 120578 proportion of players in thegame deviating from the strategy ldquoexaggeratedrdquo and select theldquorealrdquo there are
So 119909(119905)2= 0 is not the evolutionary stable strategy
In conclusion in the EGV game model the ESS is only119909 lowast (119905) = 1
The proving is over
The above analysis of stability shows that whether thepopulation of participants choose real or exaggerated aftera period of evolution all the participants will choose the purestrategymdashreal The proposed game model EGV ensures theauthenticity of all participants
53 Influence Factor Analysis of ESS According to the analy-sis in Section 4 the benefits of a node 119896 are as follows
119906 (119896) =
119881119904(0)
119881119896(0) + 119881
minus119896(0)
+
infin
sum
119905=1
[120575 (1 minus 119901)]119905minus1
lowast [120575 (1 minus 119901)] lowast 119902119894119904
lowast 119881119904(119905)
lowast
119881119896(119905)
119881119896(119905) + 119881
minus119896(119905)
minus 119881119896(119905)
(31)
We set 119881119904(0)(119881
119896(0) + 119881
minus119896(0)) = 119906(0) then we get the
optimal solution
119881lowast
119894(119905) =
(119899 minus 1) lowast [120575 (1 minus 119901)]
1198992
lowast 119862119904(119905) lowast 119875
119904(119905) lowast 119902
119894119904 (32)
Setting it into formula (31) we can get
119906 (119896) = 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
(33)
When 119899 is large enough the profit is 119906(0) This isbecause there are many vehicles competing for resourcestheir revenue is negligible and the additional income isessentially zero
Reformatting the formula (25) and putting it into the 119906(119896)provide the following
= 119909 (119905) + 01119909 (119905) [1 minus 119909 (119905)]
lowast 119906 (0) +
infin
sum
119905=1
[120575 (1 minus 119901)]119905
lowast
1198622
119904(119905) lowast 119875
2
119904(119905) lowast 119902
2
119894119904
1198992
+ [1 minus 119909 (119905)] 120572119891 + 119862119896(119905) lowast 119875
119896(119905)
(34)
Therefore the impaction factors on ESS that we can getfrom formula (34) are as follows
(1) the reward of choose real 120572
(2) the number of participants 119899
(3) themultimedia types that is the ldquoshared contributionvaluerdquo of node 119896 at the current stage 119881
119896(119905) = 119862
119896(119905) lowast
119875119896(119905)
(4) the encounter probability of the vehicles 119902119894119904
(5) the concrete analysis is in simulation part
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
10 International Journal of Distributed Sensor Networks
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
t
V(t)
(a) 119899 = 3 119862 = 5 119902 = 1
0 2 4 6 8 10 12 1405
1
15
2
25
3
35
4
45
t
V(t)
n = 2
n = 3
n = 4
n = 5
(b) Different 119899 119902 = 1 119862 = 5
Figure 4 The requester ldquosharing change contribution valuerdquo under the RGMPMW
Table 2 System parameters
Parameter ValueThe coverage of vehicle 250mThe speed of vehicle V
119894isin (5 16) ms
The distance between vehicles 119889119894119895
isin (1 5000) mThe discount factor 120575 = 098
The game ended probability 119875 = 02
6 Simulation and Analysis
61 Simulation Settings The system parameters of simula-tion settings are shown in Table 2 The vehicle is randomdistribution Vehicles that provide service probability ina slot 119905 are living service to complete the media delaysensitive services the emergency information service =1 1 1 2
62 RGMPMW Incentive Mechanism
(1) Under the Infinitely Repeated Game Nodes Reach Equilib-rium State Figure 4 shows that under the effect of RGMPMWincentive mechanism the ldquoshared contribution valuerdquo willincrease until reaching a steady state The initial state ofFigure 4(a) is competitive vehicle number 119899 = 3 theinitial ldquoshared contribution valuerdquo is 2 In the beginningthe node ldquoshared contribution valuerdquo decreases because thenode is selfish and is not willing to share their resourcesBut under the effect of RGMPMW incentive mechanismthe node realizes the selfishness will reduce its benefitSo the node begins sharing its resources and in thepicture it shows the ldquoshared contribution valuerdquo increasescontinually
After several stages of game a node ldquoshared contributionvaluerdquo tends to be stable This is because node will maximizeits own benefits and the node will increase their ldquosharedcontribution valuerdquo under the effect of RGMPMW incentivemechanism When reaching game equilibrium the benefitsof node maximizes and the node ldquoshared contribution valuerdquotends to be stable But in the next period of time the nodeldquoshared contribution valuerdquo nodes has some fluctuation thisis because the balance of ldquoshared contribution valuerdquo in eachstage game is associated with the number of competing nodesand media service type The stability of ldquoshared contributionvaluerdquo does not mean any change but a little change in eachstage game Figure 4(b) indicates that under the same initialvalue the number of competing nodes is different and thenthe stable value of ldquoshared contribution valuerdquo is differentWith the increasing of competing node number the stablevalue of ldquoshared contribution valuerdquo will decrease From (32)it can be seen when the other parameters are certain theincrease of 119899 will reduce 119881(119905)
(2) Correct and Effective IncentiveMechanism Figure 5 showsthe effectiveness of the RGMPMW incentive mechanismafter a period of incentive the node utility will reach amaximum Node will increase their ldquoshared contributionvaluerdquo for its benefit We design the RGMWMP incentivemechanism to make the nodes share their resources as muchas possible positively that is to make the node ldquosharedcontribution valuerdquo increase It can be seen from the abovetwo figures that there is a game equilibrium state whichmakes the benefit reach the maximum The correspondingldquoshared contribution valuerdquo of bigger one of two 119880(119896) fromFigures 5(a) and 5(b) is the same as the stable one fromFigure 4(b) when 119899 = 3 119899 = 5 respectively It indicates thecorrectness and effectiveness of the incentive mechanism ofRGMPMW that we design
International Journal of Distributed Sensor Networks 11
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
Figure 5 The change of node utility function in RGMPMW
0 2 4 6 8 10 12 14minus02
0
02
04
06
08
1
12
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 6 Vehicle population replicator dynamic evolution
63 EGV Game Model
(1) Validity Analysis Figure 6 shows that when the vehiclegroup has 50 vehicles select exaggeration after a period ofevolution they will be eliminated All the vehicles will selectldquorealrdquo The results show that in the vehicle in the group usethe EGV gamemodel can obtain satisfactory results It provesthat the EGV game model we proposed is effective
(2) Analysis of Influence Factors
(a) Initial Value 119909(0) As shown in Figure 7 in the vehiclegroup the larger ldquorealrdquo ratio of vehicles is at the beginningstage of EGV game the faster group ESS reaches Because ifmore vehicles select ldquorealrdquo in groups then when the vehicles
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
Select veracitySelect exaggeration
Figure 7 The impact of initial value on dynamic evolution ofpopulation reproduction
selecting ldquoexaggeratorrdquo select game opponent the probabilityof selecting real vehicle is relatively large In the game learningprocess the exaggerative will become ldquorealrdquo Therefore thevehicles group will quickly change their strategies and reachthe ESS faster
Figure 8 shows when the incentive strength is greaterthe group tends to the ESS quicker The reason is that theincentive strength is greater and can lead the vehicle to havehigher incentives In the dynamic evolution process there
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
12 International Journal of Distributed Sensor Networks
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
a = 1
a = 5
a = 8
a = 12
Figure 8The impact of incentive strength on dynamic evolution ofpopulation reproduction
0 05 1 15 2 25 30
02
04
06
08
1
t
The p
ropo
rtio
n of
stra
tegy
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
Figure 9 The impact of number of participants on dynamicevolution of population reproduction
will be more participants who choose strategies to maximizetheir own real earnings
(c) Effects of 119873 Number of Participants When the numberof vehicles in group becomes bigger that is to say the morenumber of vehicles to exaggerate then in the EGV gameit will converge more slowly to ESS as shown in Figure 9But when the number of vehicles involved in the gamereaches a certain amount in the group there was no changein convergence speed Because of the increasing number ofparticipants the learning process become very widely When
0 05 1 15 2 25 30
01
02
03
04
05
06
07
08
09
1
t
The p
ropo
rtio
n of
stra
tegy
Living service Music entertainment
Delay-sensitive serviceUrgency service
Figure 10The impact of multimedia types on dynamic evolution ofpopulation reproduction
dxdt
x
1
Figure 11
the number of participants increased to a certain extent theevolution convergence speed is no longer affected by thenumber of participants
(d) Multimedia Types Set bandwidth 119862 = 5 We putthe multimedia service divided into four types (1) the keyemergency media services such as ldquoDanger Informationrdquoand highway information 119875
119894(119905) = 09 (2) delay sensitive
services such as video conference and video service 119875119894(119905) =
07 (3) immediate complete multimedia services such asmusic and entertainment119875
119894(119905) = 05 (4) the life service such
as restaurants hotel information 119875119894(119905) = 02
As shown in Figure 10 the sharing ofmultimedia servicesis more popular the vehicles tend to stability more quicklyBecause the multimedia types not only affect the real vehicleincentives but also affect the vehicle ldquoshared contributionvaluerdquo multimedia is more popular and vehicles ldquosharecontribution valuerdquo is bigger which can also give the option ofthe real vehicle reward greater effortsThus the vehicle sharesmore multimedia popular can incentive mechanism underthe RGMPMW faster to achieve stability and the vehicleswill get more reward Group will arrive at ESS steady state asshown in Figure 10 That the vehicles will share the popularmedia more actively making emergency news media servicetimely diffusion in VANET which is the result we want
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
International Journal of Distributed Sensor Networks 13
7 Conclusions and Perspectives
In this paper we studied media services in P2P-basedVANET where all vehicles are regarded as individuals withlimited rationality We proposed ldquoMore Pay for More Work(RGMPMW)rdquo incentive mechanism to encourage vehiclenodes to share resources and studied evolutionary game toguarantee the service share veracity of all vehicles Withldquoshared contribution valuerdquo RGMPMW incentive mecha-nism accurately evaluated the contribution of each nodebased on similar manager Then as expansion to RGMPMWincentive mechanism EGV game model had been studied toprevent the mendacious service share of vehicles efficientlyThe simulation results proved RGMPMW incentive mech-anism and EGV game model are correct and effective inVANET In particular the analysis of factors ESS shows thatthe fewer the number of participants is the more urgentmultimedia services are and the faster the ESS will reachAt the same time the proposed mechanism can be welladapted to the V2V communication with high mobility andfast topology changes
We only considered the most simple P2P-based VANETscene that is one provider to several requesters In futurework we will study evolutionary game in more complicatedscene of several-to-several including variations betweennodes and unequal connection probabilities in multiplegroups
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by National Natural Science Founda-tion of China (61370201) the Scientific Research Foundationfor the Returned Overseas Chinese Scholars (45) LiaoningProvincialNatural Science Foundation ofChina (2013020019)and High-Tech 863 Program (no 2012AA111902)
References
[1] P Si F R Yu H Ji and V C M Leung ldquoDistributed multi-source transmission in wireless mobile peer-to-peer networksa restless-bandit approachrdquo IEEE Transactions on VehicularTechnology vol 59 no 1 pp 420ndash430 2010
[2] J Zhao and G Cao ldquoVADD vehicle-assisted data delivery invehicular Ad hoc networksrdquo IEEE Transactions on VehicularTechnology vol 57 no 3 pp 1910ndash1922 2008
[3] Y Zhang J Zhao and G Cao ldquoRoad cast a popularityaware contentsharing scheme in VANETsrdquo in Proceedings of the29th IEEE International Conference on Distributed ComputingSystems (ICDCS rsquo09) pp 223ndash230 June 2009
[4] K Yang S Ou H-H Chen and J He ldquoA multihop peer-communication protocol with fairness guarantee for IEEE80216-based vehicular networksrdquo IEEE Transactions on Vehic-ular Technology vol 56 no 6 pp 3358ndash3370 2007
[5] J Zhao Y Zhang and G Cao ldquoData pouring and buffering onthe road a new data dissemination paradigm for vehicular adhoc networksrdquo IEEE Transactions on Vehicular Technology vol56 no 6 pp 3266ndash3277 2007
[6] M D Dikaiakos A Florides T Nadeem and L IftodeldquoLocation-aware services over vehicular ad-hoc networks usingcar-to-car communicationrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 8 pp 1590ndash1602 2007
[7] W S Lin H V Zhao and K J R Liu ldquoGame-theoreticstrategies and equilibriums in multimedia fingerprinting socialnetworksrdquo IEEE Transactions on Multimedia vol 13 no 2 pp191ndash205 2011
[8] L Zhou Y Zhang K Song W Jing and A V VasilakosldquoDistributed media services in P2P-based vehicular networksrdquoIEEE Transactions on Vehicular Technology vol 60 no 2 pp692ndash703 2011
[9] Y Liu J Niu J Ma and W Wang ldquoFile downloading orientedroadside units deployment for vehicular networksrdquo Journal ofSystems Architecture vol 59 no 10 pp 938ndash946 2013
[10] S-I Sou W-C Shieh and Y Lee ldquoA video frame exchangeprotocol with selfishness detection mechanism under sparseinfrastructure-based deployment in VANETrdquo in Proceedings ofthe IEEE 7th International Conference on Wireless and MobileComputing Networking and Communications (WiMob rsquo11) pp498ndash504 October 2011
[11] FMalandrino C Casetti C-F Chiasserini andM Fiore ldquoCon-tent downloading in vehicular networks what reallymattersrdquo inProceedings of the IEEE INFOCOM pp 426ndash430 April 2011
[12] J Lee and W Chen ldquoReliably suppressed broadcasting forVehicle-to-Vehicle communicationsrdquo in Proceedings of the IEEE71st Vehicular Technology Conference (VTC rsquo10) pp 1ndash7 May2010
[13] A Amoroso G Marfia M Roccetti and C E Palazzi ldquoAsimulative evaluation of V2V algorithms for road safety and in-car entertainmentrdquo in Proceedings of the 20th International Con-ference on Computer Communications and Networks (ICCCNrsquo11) pp 1ndash6 July 2011
[14] J Park and M Van Der Schaar ldquoPricing and incentives in peer-to-peer networksrdquo in Proceedings of the IEEE INFOCOM pp1ndash9 March 2010
[15] L Feng and W Jie ldquoFRAME an innovative incentive schemein vehicular networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC rsquo09) pp 1ndash6 June 2009
[16] X Xiao Q Zhang Y Shi and Y Gao ldquoHow much to share arepeated game model for peer-to-peer streaming under servicedifferentiation incentivesrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 2 pp 288ndash295 2012
[17] T Chen L Zhu F Wu and S Zhong ldquoStimulating cooperationin vehicular ad hoc networks a coalitional game theoreticapproachrdquo IEEE Transactions on Vehicular Technology vol 60no 2 pp 566ndash579 2011
[18] F-K Tseng Y-H Liu J-S Hwu and R-J Chen ldquoA secure reed-solomon code incentive scheme for commercial Ad dissemina-tion over VANETsrdquo IEEE Transactions on Vehicular Technologyvol 60 no 9 pp 4598ndash4608 2011
[19] H Feng S Zhang C Liu J Yan and M Zhang ldquoP2P incentivemodel on evolutionary game theoryrdquo in Proceedings of the Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo08) pp 1ndash4 October 2008
[20] R El-Azouzi F De Pellegrini and V Kamble ldquoEvolutionaryforwarding games in delay tolerant networksrdquo in Proceedings of
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
14 International Journal of Distributed Sensor Networks
the 8th International Symposium on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo10) pp 76ndash84 June 2010
[21] C A Kamhoua N Pissinou and K Makki ldquoGame theoreticmodeling and evolution of trust in autonomous multi-hopnetworksrdquo in Proceedings of the IEEE International Conferenceon Communications (ICC rsquo11) pp 1ndash6 June 2011
[22] L Chisci F Papi T Pecorella and R Fantacci ldquoAn evolutionarygame approach to P2P video streamingrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo09)pp 1ndash5 December 2009
[23] E Altman and Y Hayel ldquoA stochastic evolutionary game ofenergy management in a distributed aloha networkrdquo in Pro-ceedings of the 27th IEEE Communications Society Conferenceon Computer Communications (INFOCOM rsquo08) pp 1759ndash1767April 2008
[24] D Niyato and E Hossain ldquoDynamics of network selectionin heterogeneous wireless networks an evolutionary gameapproachrdquo IEEE Transactions on Vehicular Technology vol 58no 4 pp 2008ndash2017 2009
[25] K Komathy and P Narayanasamy ldquoSecure data forwardingagainst denial of service attack using trust based evolutionarygamerdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference-Spring (VTC rsquo08) pp 31ndash35 May 2008
[26] J W Weibull Evolutionary GameTheory MIT press 1995[27] W H Sandholm Population Games and Evolutionary Dynam-
ics MIT Press Cambridge Mass USA 2008[28] C A Kamhoua N Pissinou J Miller and S K Makki
ldquoMitigating routing misbehavior in multi-hop networks usingevolutionary game theoryrdquo in Proceedings of the IEEE GLOBE-COMWorkshops (GC rsquo10) pp 1957ndash1962 December 2010
[29] J Coimbra G Schutz and N Correia ldquoForwarding repeatedgame for end-to-end qos support in fiber-wireless access net-worksrdquo in Proceedings of the 53rd IEEE Global CommunicationsConference (GLOBECOM rsquo10) pp 1ndash6 December 2010
[30] L-H Sun H Sun B-Q Yang and G-J Xu ldquoA repeated gametheoretical approach for clustering in mobile ad hoc networksrdquoin Proceedings of the IEEE International Conference on SignalProcessing Communications and Computing (ICSPCC rsquo11) pp1ndash6 September 2011
[31] M Afergan ldquoUsing repeated games to design incentive-basedrouting systemsrdquo in Proceedings of the 25th IEEE InternationalConference on Computer Communications (INFOCOM rsquo06) pp1ndash13 April 2006
[32] MAfergan andR Sami ldquoRepeated-gamemodeling ofmulticastoverlaysrdquo in Proceedings of the 25th IEEE International Confer-ence on Computer Communications (INFOCOM rsquo06) pp 1ndash13April 2006
[33] Y Liu J Niu J Ma L Shu T Hara andWWang ldquoThe insightsof message delivery delay in VANETs with a bidirectional trafficmodelrdquo Journal of Network and Computer Applications vol 36no 5 pp 1287ndash1294 2012
