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Cooperation Optimized Design for InformationDissemination in Vehicular Networks using

Evolutionary Game TheoryAbhik Banerjee, Vincent Gauthier, Houda Labiod, Hossam Afifi

Abstract—We present an evolutionary game theoretic approach to study node cooperation behavior in wireless ad hoc networks.Evolutionary game theory (EGT) has been used to study the conditions governing the growth of cooperation behavior in biologicaland social networks. We propose a model of node cooperation behavior in dynamic wireless networks such as vehicular networks.Our work is motivated by the fact that, similar to existing EGT studies, node behavior in dynamic wireless networks is characterizedby decision making that only depends on the immediate neighborhood. We adapt our model to study cooperation behavior in thecontext of information dissemination in wireless networks. We obtain conditions that determine whether a network evolves to a state ofcomplete cooperation from all nodes. Finally, we use our model to study the evolution of cooperation behavior and its impact on contentdownloading in vehicular networks, taking into consideration realistic network conditions.

Index Terms—Wireless Networks, Ad Hoc Networks, Vehicular Networks, Cooperative Networking, Evolutionary Games.

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1 INTRODUCTION

Packet delivery in multi-hop wireless networks dependscritically on the interaction between individual nodes.As successful transmission of a packet from a source toa destination requires forwarding by intermediate nodes,it is necessary to understand how node cooperationcan be engendered and sustained. This becomes morecrucial when considering future deployments of multi-hop wireless networks such as vehicular networks whichare characterized by high scalability and dynamicity.

In this paper, we are interested in understanding theevolution of node cooperation behavior in a wirelessnetwork. We are particularly interested in studying hownode cooperation behavior evolves in dynamic scenariossuch as that of a vehicular networks. Our primary mo-tivation is that node decision making in such contextsneeds to be spontaneous and myopic in nature, since theavailable information is limited to locally available infor-mation. Our approach is inspired from existing studiesin Evolutionary Game Theory which study evolution ofnode behavior in similar contexts.

Our motivations stem from the fact that the currenttrend in game theoretical approach in wireless networksmostly focus on optimization issues based on technical

• Abhik Banerjee is with the Department RST, CNRS SAMOVAR, TelecomSudParis, Institut Mines Telecom. 9 rue charles Fourier, 91290 Evry,France. E-mail: abhik.banerjee@ieee.org

• V. Gauthier, and H. Afifi are with the Department RST, CNRSSAMOVAR, Telecom SudParis, Institut Mines Telecom. 9 rue charlesFourier, 91290 Evry, France.E-mail: {vincent.gauthier, hossam.afifi}@telecom-sudparis.eu

• Houda Labiod is with the Department INFRES, CNRS LTCI, TelecomParisTech, Institut Mines Telecom. E-mail: labiod@telecom-paristech.fr

• To whom correspondence should be addressed.E-mail: vincent.gauthier@telecom-sudparis.eu

criteria [1] (e.g. minimization of the energy spending,and traffic maximization). However, in practice the coop-erative behavior might not be only driven by algorithmicincentives but also driven by user’s behaviors that mightjust decline to participate in the information relayingprocess as in peer to peer networks where some users(”Free-Riders”), choose not to engage for themselves inthe forwarding process. Beyond this decision based onthe local behavior of nodes, there is an intricate relation-ship between the ratio of cooperator in the network andthe information dissemination process characterized bya phase transition (e.g. too few forwarders will lead to avery restricted diffusion). To face this issue the networkas a whole needs to maintain the sufficient conditionsfor diffusion to take place. This collective behavior needto be addressed as well as the local behavior of a nodethat decides or not to participate to the forwardingprocess regardless if the decision process is taken baseon technical, or user centric concern or a mix of both.The Evolutionary Game Theory seems perfectly suitedto address these issues: first because the outcome of thegame is derived from the local decision and secondlyby the social pressure could be expressed as the ratio ofpeople sharing the same behavior.

1.1 Evolutionary Game Theory

Evolutionary game theory [2], [3] is a general theoreticalframework that can be used to study many biologi-cal problems including but not limited to host-parasiteinteractions [4], eco-systems [5], animal behavior [6],social evolution, and human language [7]. Evolutionarygames arise to study population dynamic where thefitness of individuals is not constant, but depends onthe relative abundance of strategies in the population

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pool. Originally intended for studying cooperative in-teractions in biological systems, EGT studies how thestrategy adopted by a node evolves as a result of its in-teractions with others. The framework have recently in-cluded feature like stochastic dynamics, finite populationsize, and structured populations. Indeed, the evolutionof network characteristics as a function of interactionsbetween individual nodes has become the primary focusof recent research on Evolutionary Game Theory (EGT)[8], [9] (cf. Fig. 1 for a example of EGT with a structuredpopulation). A salient property to notice is EGT doesn’tsuppose that all of the players make rational choices(i.e. a player in a EGT does not necessary adapt hisstrategy as function of his opponents’ strategies, or don’tact only toward their self-interest) as oppose to classicalgame theory. As result in EGT we are more interestedin studying the condition for achieving an evolutionarystable state (ESS) which is akin of Nash equilibrium [2].The survival of a strategy in a network depends on thebenefits achievable by it in comparison to other strate-gies. It is a well known result from EGT that in unstruc-tured populations (random encounter between nodes),natural selection favors defection over cooperation, asopposed with model with a structured population (i.e.on graphs) where cooperation is favored over defection[8]–[11]. Indeed, in structured population model wherethe interactions are constrained either by spatial or socialrelationships the emergence of cooperative behavior isfavored when the altruistic acts exceed the connectivityof a node, thereby making the cooperation on graph avaluable option in case of mild connectivity. This factis especially true in the case of scale free graph [12].Another important aspect is the problem of how thesurvival of cooperation in a social system depends on themobility of nodes in the graph, in [13] authors show thatcooperation can survive given that both the temptationto defect and the velocity at which agents move are nottoo high. In [14] authors provide new insight on a similarproblem but in the case of Public Good Games insteadof the Prisoner’s Dilemma.

1.2 Motivation for Using Evolutionary Game Theoryto Study Node Cooperation Behavior

Traditional game theory based approaches to improvepacket delivery in wireless networks typically involvedesign of utility functions that depend on multiple pa-rameters. In such scenarios, arriving at an optimal con-figuration either involves sufficient amount of availableinformation or learning over time.

Existing research on improving cooperation amongwireless nodes seeks to do so either through incentiveand punishment mechanisms or by design of detailedutility functions. While extensive literature exists on thesubject of game theory in wireless multi-hop networks,we draw attention to a few that are similar in motivationto ours. Ng et al. proposed a architecture in [15] in whichmonitor nodes impose punishments on selfish nodes to

induce cooperation. Focusing on primarily on unicastpacket routing in vehicular ad hoc networks (VANETs),Chen et al. [16] propose an incentive mechanism basedon coalitional game theory which rewards nodes thattake part in packet forwarding. Concentrating also onVANETs, Schwartz et al. studied utility function basedapproaches for improving data dissemination in [17].The authors analyze utility functions which incorporatemessage characteristics such as priority, distance to itslocation and age along with mobility information of thevehicle such as route information. A data selection al-gorithm based on similar utility functions was proposedin [18] with a view to achieving fair distribution of dataamong vehicular nodes. Shrestha et al. consider separateutility functions for Road Side Units (RSUs) and OnBoard Units (OBUs) and propose an algorithm basedon Nash Bargaining Solution to achieve large scale datadissemination in VANETs [19].

Contrasted to existing literature, we are interested instudying network scenarios where nodes do not pos-sess enough information to construct detailed utilityfunctions. Our objective here is to focus on how nodebehavior evolves in scenarios in which, not only nodeshave limited information about the network, but theirinteraction with partners nodes also change frequently.In such a scenario, it seems intuitive for nodes to makemyopic decisions based on instantaneously available in-formation. In the absence of global network information,it is plausible for nodes to choose strategies which mayonly seem to be the best, based on the limited informa-tion available, but are not optimal from the standpointof the entire network. The attractiveness of EGT forvehicular networks stems from its ability to adapt to var-ious network parameters that change over time. Further,there is a greater need for cooperation among nodes ina vehicular network for applications requiring dissem-ination of information to all nodes. In such scenarios,while node cooperation is vital to ensuring maximumcoverage for the disseminated information, the rationalchoice for any node is to receive such information but notto cooperate by forwarding it, since there are no gainsto be received by doing so. Compared to classical gametheory, an interesting aspect of EGT is that it provides away to understand how node strategies can thrive evenwhen such behavior is not rational in terms of receivedpayoffs.

A topic of particular interest for the study of coop-eration is the Public Goods Game (PGG), in which thecontributions from cooperating nodes are distributedequally among all nodes in the group. The rationalbehavior for an individual is to defect and not contributeanything to the public good, resulting in the tragedyof commons [20]. However, despite defection being theNash Equilibrium, it is observed that cooperation can notonly survive in a wide range of situations but even dom-inate at times. The conditions for cooperation in PGGshas seen extensive research focus [21]–[23]. However,to our knowledge, PGGs have not been studied in the

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context of various wireless ad hoc network deploymentssuch as VANETs. PGGs are suitable for the study of nodebehavior in wireless networks due to the prevalenceof group interactions. Further, as with PGGs, nodes inwireless networks are presented with a natural incentiveto defect.

1.3 ContributionsIn this paper, we seek to understand node cooperationbehavior in wireless networks using evolutionary gametheory. We first propose a public goods games (PGG)framework for wireless networks. The key feature ofour proposed model is to adapt existing designs ofPGGs to the unique constraints of a wireless network.Specifically, our model takes into consideration twoimportant limitations of wireless networks. Firstly, weconsider that nodes only posses information from theimmediate neighborhood. Secondly, contrasted to exist-ing definitions of PGGs, benefits of cooperation are alsorealized only from one hop neighbors. Conversely, wealso make a crucial observation that wireless multi-hopnetworks have an intrinsic ability to boost cooperationdue to implicit sharing of information as a result ofwireless broadcast advantage [24]. Subsequently, we useour model to study node cooperation behavior for theproblem of information dissemination. Finally, we focuson a realistic problem setup of content downloading invehicular networks and study how node cooperationbehavior evolves in such a scenario.

1.4 Related WorkSharing a similar motivation as ours, existing researchon wireless networks has seen some focus on algorithmdesign and analysis based on evolutionary game theory.In [25], Tembine et al. used evolutionary dynamics toanalyze node behavior over time in the context of twoproblems, namely channel access in slotted ALOHAsystems and decentralized power control. Evolutionarycoalition games were used to study the problem ofnetwork formation in [26] and [27] while dynamic rout-ing games were studied in [28]. In their work in [29],Cheng et al. studied the evolution of misbehavior amongsecondary users in a cognitive radio network.

A key aspect of our work which distinguishes itfrom existing research is the fact that we study nodecooperation behavior in the context of information dis-semination in wireless networks. Our approach aims toidentify the mutual impact that the evolution of nodecooperation and the information dissemination processhave on each other. As with the problem of informationdissemination in vehicular networks considered here,there exist other scenarios in which free-riding is the onlyrational strategy for nodes to follow. Indeed, existingresearch has explored the use of evolutionary game the-oretic techniques to study node cooperation in scenariossuch as peer-to-peer file sharing [30]–[32]. However, thedistinguishing feature of our work is that our model of

node behavior is particularly suited for wireless networkscenarios since we take into consideration aspects likenode interactions limited to immediate neighborhoodand the intrinsic ability of the wireless medium to boostcooperation.

2 PUBLIC GOODS GAMES

2.1 Overview

Public Goods Games (PGG) is a model of interaction forgroups of individuals, all of which are interested in reap-ing benefits from a shared public good. In a PGG, thebenefit available to a particular group is divided equallyamong all its members. Cooperating members contributea certain cost into the public pool. The total contributionsare then multiplied by a synergy factor r (discussednext) and divided equally among each individual inthe group, irrespective of whether it is a cooperator ora defector. The net payoff of a cooperator, therefore,is the benefit received from the PGG minus the costcontributed. A node i in a network takes part in multiplePGGs determined by the size of its neighborhood. Foreach PGG centered on each neighbor of node i, thebenefit received by i is determined by the number ofcooperators in each such group.

An important component of the PGG is the factor r,termed as the synergy factor, used to account for thesynergistic effects of cooperation. Synergistic effects ofcooperation refer to the fact that the benefits received asa result of cooperation can be greater than the sum ofthe contributed costs. The synergy factor r is a measureof the benefits obtained due to cooperation. Increasedsynergistic effects imply greater benefits received byindividual nodes compared to the costs incurred andis, therefore, more likely to induce cooperative behavior[33], [34].

Depending on the amount contributed by each coop-erator, two variants of PGGs have been studied in theliterature. In the simplest case, a cooperator contributesa fixed cost c to each PGG it is involved with. For a groupwith N participants and nC cooperators, the payoff of acooperator and a defector are, respectively,

πC = rnCNc− c

πD = rnCNc.

Each node accumulates the payoffs obtained from all itsneighboring PGGs.

A second variant of PGG considers the scenario inwhich a cooperator does not contribute a fixed amountc for each PGG they are involved with. Instead, a coop-erator i reserves a total amount c to all the PGGs it isinvolved with. Let ki denote the degree of node i, i.e. thenumber of immediate neighbors of i. Since, for a nodei with degree ki, there are a total of (ki + 1) PGGs, thecontribution made to a single PGG is c

ki+1 . Subsequently,the cooperator and defector payoffs for a node i from a

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Fig. 1. Example of Evolutionary Game in a structured population. The rules of the game. Each individual occupies thevertex of a graph and derives a payoff according to the game rules and from interactions with adjacent individuals. Ina next step the selected node change it behavior according to the outcome of the previous game played.

PGG centered at node j are obtained as,

πC =r

kj + 1

∑x∈Nj

c

kx + 1sx −

c

ki + 1

πD =r

kj + 1

∑x∈Nj

c

kx + 1sx

where sx = 1 if x is a cooperator and 0 otherwise, whileNj denotes the set of neighbors of j.

Based on the payoffs obtained, nodes update theirstrategy at each time instant by comparing their payoffvalues to a randomly chosen neighbor. If the chosenneighbor j of a node i has a higher payoff, i adoptsj’s strategy with a probability given by the followingfunction:

Pij =1

1 + exp[(πi − πj)/κ](1)

where κ denotes the intensity of selection and is usuallyset to 1.

2.2 MotivationOur choice of PGGs as the evolutionary game to for-mulate the above mentioned information disseminationproblem is motivated by direct analogies that exist be-tween the two. As with any peer-to-peer system, one ofthe primary challenges of the information disseminationproblem lies in the tendency of nodes to free-ride overthe contributions of others. As individual nodes are onlyinterested in receiving information, they can choose tonot act as forwarding nodes. However, while free-ridingis the more profitable behavior for individual nodes, theactual algorithm performance crucially depends on theforwarding behavior of nodes. A network consisting ofonly free-riders soon results in no packets being receivedby any node. Such behavior directly correlates to nodebehavior in a public goods game, in which defectionpromises higher payoffs than cooperation and therefore,is the more profitable strategy. However, a populationof all defectors soon dies off with zero payoffs as nocontributions are made. Despite the clear benefits of de-fection, however, cooperation is seen to thrive and evendominate in a wide range of scenarios. Existing studies

on evolutionary games, thus, offer a way to identifyapplication scenarios in vehicular networks in whichcooperation behavior among nodes can be expected tothrive and those in which it does not.

3 A PUBLIC GOODS FRAMEWORK FORMULTI-HOP WIRELESS NETWORKS

As outlined earlier, a public goods game presents anattractive method of accurately modeling node cooper-ation behavior for the information dissemination prob-lem. However, the nature of packet transmissions in amulti-hop wireless network imposes restrictions whichlimit the amount of payoff available to a node. As aresult, the classical definition of PGG cannot be useddirectly. In order to understand how node cooperationbehavior in a multi-hop wireless network evolves overtime, we formulate a public goods framework takinginto consideration the constraints imposed by a wirelessnetwork in determining node payoffs. Subsequently, weuse simulation results to identify the impact of increasein the synergy factor and node mobility on the levelof cooperation in a network. The results presented inthis section and the next focus on the node cooperationbehavior in the steady state. The steady state refers to thelong term behavior to which the nodes in the networkconverge to.

3.1 Adapting PGG to Multi-hop Wireless NetworksOur approach aims to define the payoff received by anode in a single time slot. We use the second variant ofPGG defined earlier as a baseline since it incorporatesdiversified contributions from each cooperator. Such adesign is suited especially for broadcast protocols inwireless networks since a single transmission from anode is sufficient to reach all its neighbors. The contribu-tion of a cooperating node, thus, does not grow with thenumber of neighbors, but stays constant. Considering thetransmission of a packet within a single time slot as theunit cost, this is the maximum cost a cooperator can con-tribute in a time slot. However, the likelihood of a nodetransmitting in a slot is determined by the contention

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in its neighborhood. The contribution of a node, thus,depends on its degree. We express the contribution of acooperator i as c

ki+1 , where ki is the degree of i and cis the constant cost per contribution, taken equal to 1 inthis paper since we consider the transmission in a timeslot to be of unit cost.

A second distinguishing factor is that, as any transmis-sion from a node can only be received by its immediateone hop neighbors, a cooperator only contributes to thegame centered on itself. In the traditional definition ofPGG, a node takes part in games centered on all nodesin its neighborhood and subsequently receives benefitscontributed by cooperators in each of the games. Sucha model is not suitable for multi-hop wireless networksince contributions from nodes more than one hop awaycannot be immediately realized by a node. Moreover, inany time slot, a node only makes a single contribution.In our game formulation, the benefits received by anode i consist only of the contributions made by eachcooperating neighbor j for the game centered on itself.We express the payoff received by a node x at any timeslot in terms of the traditional definition of PGG as,

πx = r∑

y∈(Nx∪x)

∑z∈(Ny∪y)

c

ky + 1qy −

∑y∈(Nx∪x)

c

kx + 1qx

(2)Here, the inner summation of first term and the summa-tion of the second term correspond to the games centeredon all the neighbors of a node. The distinction from thetraditional definition of PGG is made by the variable qiwhich takes the value 1 only if i is a cooperator for agame centered on itself, and 0 otherwise.

Note that the benefits are not divided by the neigh-borhood size due to the fact that only a single gameis played. Here, we make the observation that, as asingle transmission is sufficient for sharing informationwith all nodes within a neighborhood, synergistic effectsexist implicitly in a wireless network. The sum of thebenefits received by all nodes in a neighborhood isalways likely to exceed that of the total cost incurred.Thus, the synergy factor r in the above formulationrepresents the additional benefits that can be realizeddepending on network conditions. In this context, weenvision r as representing benefits achievable to a nodein addition to the number of received packets. Thus, rmay be used to quantify other aspects of network flowsuch as traffic priority in terms of either the importanceof the information content or prioritization with regardto network costs.

3.2 Evolution of Node Cooperation Behavior

We obtain simulation results to identify the impact of thesynergy factor and node mobility on the level of coopera-tion. Fig. 2 shows the expected fraction of cooperators inthe steady state. The results are presented for increasingvalues of the synergy factor r normalized by the averageneighborhood size in the network (〈k〉+ 1).

0.2 0.4 0.6 0.8 1.0 1.2 1.4Synergy η (η= r⟨

k⟩ )

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Fig. 2. Impact of node velocity and synergy factor on thefraction of cooperators in the steady state.

As with most existing studies on public goods games,cooperation is seen to dominate for high values of thesynergy factor. This results form a high benefit to costratio, due to which the cost incurred by cooperatorsbecomes negligible to the overall payoff received. Wenote that cooperation can be sustained when the nor-malized synergy factor η ≥ 0.6 for a static network.This is similar to existing results on PGGs with diver-sified contributions from cooperators. However, in PGGformulation adapted to wireless networks above, twoopposing factors are present. As nodes only play a singlegame in their neighborhood, this acts as a mitigatingfactor from the point of view of enhancing cooperation asnodes do not accumulate benefits from games centeredon other nodes in their neighborhood. This mitigatingfactor, though, is countered by the implicit synergisticeffects existing in a wireless network, which act toincrease the benefits available to a node.

Increase in node velocity shifts the domination ofcooperative behavior to higher values of synergy factor.This results from the fact that, for low to moderately highvalues of synergy, node cooperation behavior is morelikely to survive in neighborhoods that have a higherfraction of cooperators. For increasing node velocities,neighborhood structures change frequently leading tobreakdown of clusters of cooperators. This results in ahigher likelihood of defection emerging as the dominat-ing strategy. This effect vanishes at higher values of thesynergy factor since the cost component of the payoffbecomes negligible compared to the benefit received bya node. As a result, cooperators are less likely to switchto defection upon comparing payoffs with neighborhooddefectors. The result in figure 2 show a sharp shiftfrom a network state where almost all the nodes havea tendency to defect to a state where almost all ofthem cooperate. This is suggesting that the responseof the model has a tipping point, when it is passed itindicate that the network will induce propel a changein behavior into the network. This is also suggesting

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that once the change in behavior is triggered the systembecome resilient to local change in the network structureand local behavior shift. As consequence the evolutionthe of cooperation in the model is only being lightlyaffected by the velocity of node and the rate of changein the network topology.

4 PUBLIC GOODS GAMES FOR INFORMATIONDISSEMINATION IN MULTI-HOP WIRELESS NET-WORKS

Using the basic framework of public goods games de-fined in the previous section, we now formulate a PGGto model information dissemination. Efficient delivery ofdata packets in a multi-hop network depends criticallyon the set of intermediate nodes which are willing to actas forwarding nodes. In dynamically changing networkssuch as vehicular networks, this is compounded by thechanges in network topology. Our objective is to studythe conditions which allow for packet delivery perfor-mance to adapt to the level of cooperation. We considera basic information dissemination problem first, basedon which we formulate the game structure and presentanalytical and simulation based insights on evolutionof node cooperation behavior. In the next section, weuse this formulation to study how node cooperation andinformation dissemination proceed in tandem in a morerealistic setup.

4.1 System Model

4.1.1 Problem DefinitionThe problem setup we consider is that of a network inwhich M packets are to be disseminated. The packetsare generated by individual source nodes, all of whomare cooperators initially. All nodes in the network areinterested in receiving all of these M packets. However,since a node is only interested in receiving, it may notchoose to forward them to other nodes, thereby adoptinga free-riding behavior. As successful dissemination ofthe packets relies on the number of nodes willing toforward, a tradeoff exists between node behavior andpacket delivery performance.

4.1.2 Packet Transmission AlgorithmThe packet transmission algorithm proceeds as follows.Nodes buffer all packets they receive. Upon deciding toact as a cooperator, a node randomly chooses from theset of packets it has not yet transmitted and schedulesit for transmission. If there are no new packets to betransmitted, any one of the packets is retransmitted.Allowing retransmission of packets is useful for dynamicscenarios such as in the case of mobility.

4.1.3 Mobility ModelWe first use a model in which all nodes move with aconstant velocity v in randomly chosen directions. Thus,

at any time t, the coordinates of a node i is given relativeto its position at time (t− 1) as,

xi(t) = xi(t− 1) + v cos θi

yi(t) = yi(t− 1) + v sin θi

where the angle of movement θi is randomly chosen ineach time slot.

4.2 FormulationWhile the above discussion outlines a framework forformulation of public goods games in wireless networks,we now look at individual aspects of the game formu-lation pertaining specifically to the problem of networkwide dissemination of M packets. We elaborate furtheron specific aspects of the game formulation.

As outlined earlier, the benefits obtained by nodes in aPGG map to the number of packets received in the caseof information dissemination. The game dynamics aredetermined by the payoffs received by a node in eachtime slot and the resulting strategy updates. Here, thebehavior of information exchange in wireless networksdiffers somewhat from how benefits are obtained in aPGG and payoffs realized. The difference results fromthe fact that while the payoffs based on neighborhoodcontributions are instantly realized in a PGG, the same isnot true with packet transmissions in wireless networksdue to node contention behavior. A packet transmittedby a node can only be received correctly by its neighborsif no other nodes are transmitting simultaneously withinthe same neighborhood, as doing so would result incollisions. Thus, actual transmission of a packet is likelyto take place later than the time when a node decidesto enqueue a packet for transmission by acting as acooperator. This leads to a dilemma with regard to howthe benefits were realized. For instance, consider a nodeA that chooses to act as a cooperator and enqueue apacket at a time t, which eventually gets transmitted attime t + τ . In this intervening time period τ , however,it is quite likely that the A decides to switch its strategybased on neighborhood observations of payoffs. Thus,when the packet transmission actually takes place, A’sstrategy is actually that of a defector or a free-rider. Thiscould give rise to inconsistencies in the game dynamicsas neighbors of A may decide on their strategies basedon observation of A as a defector, which is a false notionsince the packet transmission actually took place becauseof A’s behavior as a cooperator. Further, there is theadditional question of whether, as with the traditionaldefinition of PGGs, payoffs should be updated duringthe time period (t, t+ τ).

We take the above mentioned factors into considera-tion for formulating the PGG. One way of characterizingsuch a scenario would be to consider the expecteddelay between a node’s decision to cooperate and actualtransmission of the packet. Alternatively, as with thevariants of PGG described earlier in 2, a node canbe expected to make contributions in each time slot it

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is a cooperator, with the contribution obtained as theprobability of transmitting in each slot. The transmissionprobability can be obtained in terms of the number ofcontending nodes, which, in a saturated scenario, is theentire node neighborhood, and thus correlates directly tothe contributions from cooperators in the second variantof PGG. Considering fair random scheduling of nodes,the cost incurred by a cooperator i in a single time slotcan be given as,

ηi =c

ki + 1(3)

where ki is the degree of node i. As i has equal chancesof transmitting in each of the τi = (ki + 1) time slots,the total contribution made by a node is proportionalto how long it stays a cooperator. Thus, if it staysa cooperator throughout the τi slots, the contributionequals 1. Therefore, the total benefit received by a nodein a single time slot is the aggregation of contributionsfrom all cooperators in its neighborhood, and can beexpressed as,

bi =r

ki + 1

∑j∈Ni∪i

c

kj + 1sj

where Ni denotes the set of neighbors of i and sj = 1 ifj is cooperator and 0 otherwise. A normalization factorr

ki+1 is introduced to take into account the impact ofcontention of the neighborhood of i, in addition to thecontention experienced by each node j. Subsequently,the payoff received by a node i depends on whether itis a cooperator or a defector,

πDi = bi

πCi = bi − ηi (4)

An important difference of the above formulation withthe traditional definition of PGG is that the payoff of anode is only the result of the game centered on itself.Such a design is due to the fact that nodes only receivepackets transmitted in their immediate neighborhood.

Next, we make the observation that, while the aboveformulation correlates directly with node contributionsin a saturated scenario, the same is unlikely to be true forthe packet dissemination problem under investigationsince the set of contending nodes only includes coop-erators. Thus, equation (3) can be rewritten as,

ηi =c

nCi + 1(5)

where nCi denotes the number of cooperators in theneighborhood of i. As outlined earlier, the benefits inPGG correspond to the reception of packets. In a PGGcentered at node i, the total benefit received is equal tothe total of the contributions made by each cooperatormultiplied by a factor r. In the case of the informationdissemination, however, a packet received by a nodeis only meaningful if it has not been received earlier.Thus, the only cooperators in a node’s neighborhood thatmatter are those that have at least one new packet to

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[P1, P2, P3]

[P1, P2, P3, P5] [P1, P2, P3, P4]

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[P1, P4, P5, P6]

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Fig. 3. Figure showing direction of flow of benefits fromcooperators depending on the reception status of nodesin a graph. Darkly shaded lines with arrows indicate edgeswith flow of benefits. Lightly shaded lines indicate edgeswith no flow of benefits. Lightly shaded dashed lines showedges among defectors.

transmit. Based on this, we rewrite the benefit receivedby a node i as follows

bi =r

nCi + 1

∑j∈Ni∪i

c

nCj + 1tj (6)

where tj = 1 if j is a cooperator and has at least onepacket to transmit which has not yet been received by iand 0 otherwise. The neighborhood of i is denoted byNi.Subsequently, the payoffs are expressed as in equation(4).

The above game formulation allows us to map thegame behavior directly to that of information dissemi-nation. The number of packets received by a node, thus,correlate to the total benefits accumulated over time bya node.

The payoffs defined in equation (4) refer to the in-stantaneous payoffs corresponding to the reception per-formance in a single time slot. The instantaneous payoffvalues are used for strategy update by nodes.

4.3 Conditions for Node Strategy Evolution

To gain an understanding of how node behavior evolves,we obtain conditions under which the game formulationin section 4.2 can lead to growth of cooperation in a net-work. To do so, we look at the neighborhood conditionsthat induce a node to change its behavior from that of adefector to a cooperator.

4.3.1 Conditions for Inducing Cooperation in Static Net-workConsider a node i that acts as a defector at time t.The behavior of i at time (t + 1) is determined by thedifference in payoffs of itself and its neighbors. Let ki bethe degree of i, xi the fraction of neighbors which arecooperators and ui the fraction of cooperators that areuseful to i. As defined earlier, ui is determined by the

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set of packets already received by i at time t. The payoffof i at time t can, thus, be written as,

πDi =1

(xiki + 1)

uixiki(x(t)〈k〉+ 1)

(7)

where x(t) is the fraction of cooperators at time t in thenetwork and 〈k〉 is the average node degree. Transitionof i’s strategy to that of a cooperator at time (t + 1) isproportional to the difference in payoff πCj of a cooper-ating neighbor j with πDi . As with i, the payoff of j isdetermined by the set of cooperators in its neighborhoodwhich have packets to transmit not yet received by j, andcan be given as,

πCj =1

(xjkj + 1)

ujxjkj(x(t)〈k〉+ 1)

− 1

(xjkj + 1)(8)

The probability that i becomes a cooperator is propor-tional to the payoff difference, which can be expressedas,

pi(D → C) ∝ 1

(x(t)〈k〉+ 1)

(ujxjkj

(xjkj + 1)− uixiki

(xiki + 1)

)− 1

(xjkj + 1)(9)

The above discussion shows that j is more likely toinduce cooperative behavior if it is likely to receive newpackets from cooperators in its own neighborhood. Co-operative behavior is, thus, likely to grow from regionsof high concentration of cooperators coupled with highdiversity of source packets. Further, a high value of thesynergy factor r mitigates the role of the cost incurredby a cooperating node.

While the above discussion outlines the conditionsthat determine whether node i changes its strategy, theprobability qji(t) that a neighbor j contributes to i’spayoff at time t depends on the set of packets alreadyreceived by each node. Let mi and mj denote the numberof packets already received by i and j respectivelyat time t. The probability qji(t) is determined by thefollowing lemma:

Lemma 1: The probability that a node j contributes tothe benefits received by a neighbor i is given as

qji(t) =

{x(t), if mj > mi

x(t)[1−

(cj(kj−1)

kj

)mj]

, otherwise.(10)

where cj is the clustering coefficient of j, ki and kj arethe node degrees of i and j respectively.

Proof:

(a) The first part of the result is obtained trivially as thecondition mj > mi implies that j has more packetsthan i and the probability that it contributes to i’spayoff is that it is a cooperator.

(b) When mj ≤ mi, qji(t) is the probability that jreceives at least one packet not received by i in thetime period [0, t]. To understand this, we make ob-servations about how packet dissemination proceeds

in a static network. As the neighborhood of a nodedoes not change with time, any broadcasted packetcan only be received by a node if it is forwarded byany one of its neighbors. Two neighboring nodes iand j can, therefore, receive the same packet if itis broadcasted by a node which is a neighbor toboth. Alternatively, j can receive a packet from anode which is not a neighbor to i and therefore, idoes not receive it. 1 Thus, the probability that bothi and j receive the same packet from a node b is theprobability that b is a neighbor to both, which canbe given in terms of the clustering coefficient as

pcommonij = cj(kj − 1)

kj.

Thus, the probability that all packets received by jare also received by i is (pcommonij )mj . The probabilitythat j contributes to i’s payoff is that it has receivedat least one packet which has not yet been receivedby i and thus, equation (10) follows.

To further understand the implication of Lemma 1on node cooperation behavior, we make the observationthat node interactions in this context are comprised oftwo aspects, namely, (a) the influence a node has onthe payoff of its neighbors, (b) the influence of a nodeon the changes in strategy of its neighbors. Lemma1 directly shows how observation (a) is impacted bythe neighborhood structure of a node, measured as theclustering coefficient. However, a further inference canbe drawn from Lemma 1 in relation to observation (b).A high clustering coefficient cj implies that j shares agreater part of its payoff with its neighbors, implyinglow difference in payoff values. Thus, the probabilitypi(D → C) in equation (9), for a defecting neighbor iof j, to switch to a cooperating behavior by comparingits payoff to j redcues with increasing cj . An extremecase, therefore, is when Nj ⊂ Ni, Ni and Nj being theset of neighbors of i and j, in which case j can neverinfluence i.

4.3.2 Conditions for Cooperation Growth with MobilityIn a network with mobile nodes, node cooperation be-havior is impacted due to the constant churning of nodeneighborhoods. As discussed earlier in section 4.3.1, theevolution of node cooperation behavior in a networkis determined by how the node interactions impact (a)instantaneous payoffs, (b) strategy updates.

In section 4.3.1, we noted how the clustering coeffi-cient of a node determines node behavior in its neigh-borhood. In a mobile scenario, however, the cluster-ing coefficient cannot be directly correlated as it keepschanging due to constant changes in the neighborhood

1. There is a third possibility here, which is that i receives the samepacket from another neighbor a which is not a neighbor of j. However,this implies that the packet reached both j and a without reaching i.The probability of this scenario is quite low [35, Fig. 1] and hence wedo not include it as part of this discussion.

9

1 2 3 4 5 6 7 8 9 10Velocity v

0.0

0.2

0.4

0.6

0.8

1.0Probability of Meeting

pOld-SimpNew-SimpOld-AnalpOld-Sim

Fig. 4. Probability of meeting a new neighbor after makinga jump.

of a node. Since the payoff of a node is determined by thenumber of useful cooperators in its vicinity, it can receivehigher payoffs if it meets cooperators with new packets.Existing research has shown [36], [37] that mobility canhelp improve packet delivery performance by reducingthe number of hops required. For the problem underconsideration too, mobility can impact node cooperationbehavior due to changes in the neighborhood structureof nodes. Meeting a higher number of new nodes in eachtime step, which are likely to have new packets not yetreceived by a node, is likely to result in higher payoffscompared to maintaining the same set of neighbors. Weanalyze how mobility impacts the set of neighbors of anode in each time step.

For the mobility model used above, the jump lengthfor a node i at any time step t is a constant distancev. The set of neighbors of i as a result of this jump attime (t + 1) is determined by the jumps made by othernodes in the network, also of length v. The payoff of i at(t+1) increases if a greater fraction of its neighborhoodconsists of nodes which were not neighbors at t.

The probability that any neighbor j of i at time t is alsoa neighbor at (t+1) is the probability that i and j are lo-cated close enough to communicate with each other, i.e.they are located within each other’s transmission rangerad. Considering N nodes distributed uniformly over acircular region of radius R, the probability that a nodei meets an existing neighbor, pnbrold , and the probabilitythat it meets a new node, pnbrnew are respectively obtainedas,

pnbrold =

∫ rad

0

∫ 2π

0

cos−1( v2+rad2+d2

2vd)

π

1

2πdθ

2x

rad2dx

pnbrnew =

∫ R

rad

∫ 2π

0

cos−1( v2+rad2+d2

2vd)

π

1

2πdθ

2x

(R2 − rad2)dx

(11)

where d =√v2 + x2 − 2xv cos θ. Subsequently, the

probabilities that, among the set of neighbors of i at

1 2 3 4 5Synergy r

0.00

0.05

0.10

0.15

0.20

0.25

Velo

city

v (

m/s

)

0.0

0.5

1.0

Fig. 5. Impact of synergy and velocity on node coopera-tion.

(t+ 1), a randomly chosen node is an old neighbor or anew one can be obtained respectively as,

fold =pnbrold rad

2

pnbrold rad2 + pnbrnew(R

2 − rad2)

fnew =pnbrnew(R

2 − rad2)pnbrold rad

2 + pnbrnew(R2 − rad2)

(12)

A higher fraction of new neighbors, fnew > fold, impliesa higher number of useful cooperators in the neigh-borhood of a node resulting in a higher payoff. Anysuch node, thus, is more likely to influence strategiesin its neighborhood. The variation of fnew and fold withincrease in velocity is shown in Fig. 4. As can be seen, ahigher node velocity increases the likelihood of meetingnew nodes, which in turn can lead to higher payoffs asdiscussed earlier.

4.4 SimulationWe use simulation results to understand the impactof node cooperation behavior on the information dis-semination performance. We first run simulations on auniformly distributed spatial network of 300 nodes andobserve the evolution of node behavior and algorithmperformance over time averaged over 50 simulationruns.

Each simulation run starts by randomly choosing aset of nodes as source nodes, each of which generatesa single packet to be broadcasted to all nodes in thenetwork. Initially, only the source nodes are cooperators.Subsequently, at each time instant, nodes determine theirstrategies based on payoffs obtained as per the gameformulation in 4.2. Each time slot is assumed to consist ofa single packet transmission. Nodes attempt to forwardbuffered packets only when they choose cooperation asa strategy. The payoffs are calculated as described ineq. 4. The simulation is run till either all nodes use thesame strategy or the information dissemination processis completed, i.e. all packets have been received by allnodes.

10

Fig. 5 shows how node cooperation in the steady stateis determined by values of r and v. Compared to thebasic PGG framework formulated in section 3, mobil-ity is seen to enhance node cooperation significantly.This results from the fact that, in the PGG formulationadapted for information dissemination, node payoff isa function of the number of useful cooperators and notjust the number of cooperators. As mobility speeds upthe information dissemination process, nodes are morelikely to encounter cooperators holding new packets andare thus ’useful’, leading to higher payoffs and morechances of cooperative behavior.

5 NODE COOPERATION BEHAVIOR FOR CON-TENT DOWNLOADING IN VEHICULAR NET-WORKS

We now study node cooperation behavior in the contextof content downloading services in a vehicular network.Content downloading services are likely to grow inpopularity in future vehicular networks. Applicationsare likely to range from traffic related information suchas safety and route information to user specific mediacontent. Similar to existing studies [37]–[39], we considera scenario in which all vehicular nodes are interested indownloading content from a single service provider. Thecontent dissemination is done by the service provider bydistributing them to a set of seeder nodes. The seedernodes then broadcast the packets to their immediateneighbors, which in turn choose to relay them to othernodes depending on their cooperation strategy. The nodestrategy evolution follows the same PGG formulation insection 4.2.

5.1 Network Model

We consider a network of N mobile nodes, all of whomare interested in receiving a set of M packets from acontent service provider. The nature of the content itselfcould depend on the type of vehicular application. Forinstance, a large media file could be composed of Mchunks. Alternatively, each packet could correspond toindividual pieces of information in which all nodes areinterested. We consider a scenario in which the serviceprovider distributes all of these packets to a set of seedernodes distributed randomly in the network. At each timeslot, a seeder transmits a randomly chosen packet fromthe set of M packets to its immediate neighbors. Dis-semination to the rest of the network is determined bythe relaying behavior of non-seeder nodes and therefore,depends on the evolution of node cooperation in thenetwork. As in section 4, the strategy adopted by a nodeat each time slot depends on the payoff obtained byits immediate neighbors, determined by the number ofuseful cooperators in the neighborhood.

A similar setup was considered in [40], where a smallsubset of nodes in the network receive content directlyfrom the service provider. Packet forwarding is limited

100 101 102

Distance [m]

10-3

10-2

10-1

100

P(X

> x

)

100 101 102

Pause Time [mins]

Fig. 7. Levy walk model used in our simulations, we plotan example with the velocity of node set to 5m/s, (cf. Table1 for more information about the other parameters)

to a set of helper nodes, which includes nodes receiv-ing content directly from the service provider, whilethe rest of the nodes in the network are marked assubscribers which only receive packets. However, theimpact of evolution of node strategies is not studiedin [40]. We focus on how information dissemination isimpacted when nodes are allowed to switch strategiesdepending on the payoffs received. A key difference withthe scenario in section 4 is the presence of a dedicated setof seeder nodes which always maintain their strategy ascooperators. Such a provision is necessary since seedernodes always begin with the complete set of packets.Therefore, allowing them to change strategies using thePGG formulation would immediately result in themacting as defectors, thereby halting the disseminationprocess. Moreover, from the perspective of practicalapplication, this corresponds to a scenario in which aservice provider deploys seeder nodes to improve datadelivery performance at receivers.

All nodes move according to the Levy Walk mobilitymodel [41], [42]. While a majority of existing researchhas illustrated the accuracy of Levy Walks in predictinghuman mobility, recent research has shown that thesame is also true for vehicular mobility [40], [43], [44].Moreover the study of cities road networks in [45],[46] show that the typical distance `1 between nodesintersection scale as P (`1) ∼ `−γ1 suggesting that LevyWalk will be a meaningful approximation (given theexistence a cutoff) of the jump length distribution of carsfrom intersection to intersection in a roadmap. Hence,adopting such a model presents a realistic setup forstudying node cooperation behavior in the presence ofmobility (cf. Fig. 7).

5.2 Simulation ResultsOur simulation setup consists of a network of 400 nodes,a subset of which are seeders. We obtain results fordifferent values of the number of seeders in the net-work. We run simulations on a more realistic setup ofrandomly distributed nodes in which the neighborhood

11

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Synergy η (η= r⟨

k⟩ )

0

2

4

6

8

10

12

14Velocity (m/s)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

(a)

0.2 0.4 0.6 0.8Synergy η (η= r⟨

k⟩ )

0.0

0.2

0.4

0.6

0.8

1.0

Fract

ion o

f co

opera

tors

Static

Velocity = 10 m/s

(b)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Synergy η (η= r⟨

k⟩ )

0

2

4

6

8

10

12

14

Velo

city

(m

/s)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

(c)

0.2 0.4 0.6 0.8 1.0Synergy η (η= r⟨

k⟩ )

0.0

0.2

0.4

0.6

0.8

1.0

Fract

ion o

f co

opera

tors

Static

Velocity = 10 m/s

(d)

Fig. 6. Node cooperation level in the steady state, (a) for the case of a networks with 30 seeders, (b) subset of thesimulations with velocity 0 m/s and 10 ms/s for the case of 30 seeders, (c) full set of simulation for the case of anetworks with 60 seeders,(d) subset of the simulations with velocity 0 m/s and 10 ms/s for the case of 60 seeders.The initial fraction of cooperator in Fig (b) and (d) account from the fact that the seeders are alway cooperator

of each node is determined by its transmission range. Weused the quasi unit disk model where Pc the probabilityto connect to neighbor node is given relative to theirdistance x (cf. eq. 13),

Pc(x) =

1 iff x < Rinner1− ( Router−x

Router−Rinner)ζ iff Router ≥ x ≥ Rinner

0 iff x > Router(13)

In order to allow for errors in calculation of payoffs ina realistic scenario, we include a gaussian noise param-eter which introduces a certain degree of randomness,

πDi = bi +N (0, σ)πCi = bi + ηi +N (0, σ)

(14)

The parameter values used in the simulation are listedin Table 1.

Fig. 6 shows the impact of the number of seeders onthe node cooperation level in the steady state. Increas-

ing the number of seeders results in a higher level ofcooperation in the network. This is an expected resultas more seeders implies faster dissemination of packetsin the network, thereby leading to higher likelihood offinding ’useful’ nodes. Thus, cooperating nodes have ahigher probability of influencing neighborhood behavior.A surprising observation, however, is that, in the η − vregion in which cooperation dominates, the actual levelof cooperation is higher when the number of seeders islower. This results due to the fact that, while increasingthe number of seeders results in a higher likelihood ofcooperative behavior, this is accompanied by faster dis-semination of information. Thus, nodes quickly receivethe entire set of packets they are interested in. A smallfraction of nodes are, thus, likely to stay non-cooperative.However the cooperation level remain only mildly im-pacted by the mobility of users (in the reasonable rangesimulated in this simulation).

12

10-4

10-3

10-2

10-1

100

Vel

ocit

y =

0

(A)

r = 0.5

(B)

r = 1.0

(C)

r = 1.5

(D)

r = 2.0

10-4

10-3

10-2

10-1

100

Vel

ocit

y =

1(E) (F) (G) (H)

10-4

10-3

10-2

10-1

100

Vel

ocit

y =

5

(I) (J) (H) (K)

10-4

10-3

10-2

10-1

100

Vel

ocit

y =

10

(L) (M) (N) (O)

0 25 5010-4

10-3

10-2

10-1

100

Vel

ocit

y =

15

(P)

0 25 50

(R)

0 25 50

(S)

0 25 50

(T)

(a) 60 seeders

10-510-410-310-210-1100

Vel

ocit

y =

0

(A)

r = 1.0

(B)

r = 2.0

(C)

r = 3.0

(D)

r = 4.0

10-510-410-310-210-1100

Vel

ocit

y =

1

(E) (F) (G) (H)

10-510-410-310-210-1100

Vel

ocit

y =

5

(I) (J) (H) (K)

10-510-410-310-210-1100

Vel

ocit

y =

10

(L) (M) (N) (O)

0 50 10010-510-410-310-210-1100

Vel

ocit

y =

15

(P)

0 50 100

(Q)

0 50 100

(R)

0 50 100

(S)

(b) 30 seeders

Fig. 8. The figures (a) and (b) show the evolution of distribution of packets received by nodes across different velocityand synergy factor (r). Both figures showed that both factors greatly improve the spreading efficiency of the packetsacross the networks, from weak diffusion of packets in fig. (a).A to almost full diffusion in fig. (a).T (the same is truefor fig (b).A and (b).S respectively). In fig (a) the diffusion append for lower synergy factor than in fig (b) due to the factthere are twice the number of seeders. The buffer size for fig. (a) is 50 packets and for fig. (b) 100 packets. In fig (a) inthe case of 60 seeders for r > 2 we achieved full diffusion in almost all the cases

In Fig. 8 we show the joint effect cooperation leveland the dissemination process through the cumulativedistribution of the number of packets received by nodesacross the network. The ECDF shifts towards the rightfor higher values of r and v signifying improved dis-semination of packets as nodes are more likely to getall packets. We show here that the mobility and thecooperation level (r stands for the synergy factor) haveboth a great impact on the speed of dissemination pro-cess through the networks. The same phenomenon is

observed in Fig. 9, and Fig. 10, in both cases we shownhow the set of packets pending to be delivered evolve asfunction of the velocity and the cooperation level. In Fig9 we show that the number of packet remaining to bedelivered decrease as function of both R (the cooperationlevel), and the number of seeders. In Fig 10 in the caseof 30 seeders, we can observe a sharp decrease of thenumber of packets pending to be delivered for differentr values, indeed in 10(a) and 10(b) the number of packetsstay stable over different velocities but in 10 (c) and

13

TABLE 1Simulations Parameters

Parameters Value Parameters ValueSimulations Parameters Levy-walk Parameters

Size of simulation area 1000.0 m2 α 0.9Number of node 400 β 0.9Simulation length 300.0 s velocity [0 .. 15.0] m/sNumber of seeder [30, 60] Quasi-unit-disk Parameters

Buffer size [50, 100] ζ 0.3PGG Parameters Rinner 40.0 m

Initial cooperator ratio 0.5 Router 75.0 mNoise variance (σ) 0.1

r = 1.0 r = 2.0102

103

104

105

106Seeder =30, Velocity = 5

r = 1.0 r = 2.0

Seeder =60, Velocity = 5

Fig. 9. Number of packets remaining to be delivered fordifferent number of seeder.

10 (d) once a given value a the threshold value of r iscrossed the number of packet drops significantly and theinformation dissemination took place for almost all thenodes in the network.

5.2.1 Simulation CodeThe code used in this paper is available at [47]

5.3 Comparison with Classical Game Theory basedApproachesThe motivation for the choice of an evolutionary gametheory based approach was discussed earlier in section1. To particularly highlight the benefits of our proposedmodel in the context of content downloading in vehic-ular networks, we draw comparison with approachesin existing literature that use classical game theory insimilar deployments. In [17], a node computes the utilityof each data file by taking into consideration the vehiclemovement details such as the route and velocity and alsocharacteristics of the data such as priority, size, age andgeographical region. Two vehicles that encounter eachother determine the set of packets to exchange using analgorithm based on Nash Bargaining. The same authorspropose a similar approach in [18] with the objective ofachieving fairness in data dissemination. Shrestha et al.

v = 1 v = 5 v = 10 v = 15102

103

104

105

106Seeder = 30, r = 1

(a)

v = 1 v = 5 v = 10 v = 15102

103

104

105Seeder = 30, r = 2

(b)

v = 1 v = 5 v = 10 v = 15101

102

103

104Seeder = 30, r = 3

(c)

v = 1 v = 5 v = 10 v = 15100

101

102

103Seeder = 30, r = 4

(d)

Fig. 10. Number of packets remaining to be delivered forvarious parameters v and r

proposed a utility function based on packet prioritiesin [19] and subsequently evaluated the performance ofdifferent bargaining algorithms.

A primary distinguishing feature of our proposedmodel with the above approaches is the localized natureof the information, both from the spatial and tempo-ral perspectives. Not only is the information requiredlimited to the immediate neighborhood, nodes are alsoassumed not to have any predetermined knowledgesuch as vehicle routes, packet priorities, etc. as all suchinformation itself may be dynamic. Allowing myopicnode decision making allows us to study how the net-work state determines its behavior in the succeedingtime period. We envision this study to be useful from thepoint of view of planning for information disseminationin vehicular networks. For instance, in the scenario

14

considered in section 5, seeder nodes may choose theset of packets to transmit depending on their immediateneighborhood, so as to maximize dissemination. Further,while the proposed model only takes into considerationpacket reception status at nodes, it can be enhanced toaccommodate other factors which can play a role in nodedecision making. For instance, factors such as residualenergy may determine a node’s forwarding behavior,which can be included in the model.

6 CONCLUSION

We introduce in this paper a framework based onEvolutionary Game Theory to study the evolution ofnode cooperation in wireless ad hoc networks. Afterintroducing the general feature of the EGT, we proposeda model of node cooperation behavior that adapts PublicGoods Games to the specifics of wireless ad hoc net-works. Further on, we described in which conditionsnetworks could evolve and sustain a state of near to fullcooperation among the devices. Our main contributionin this work is aimed at demonstrating the joint effectsof the cooperation and the mobility rate on the spreadof the information in wireless multi-hop networks. Tofully take advantage of a rapid dissemination processin a rapidly changing environment we show that weneed to exploit in tandem both the mobility and self-propagating property of the EGT to enable control ofthe node behavior. We also show how the success ofthe resulting diffusion process depends on the natureof the interactions between this two properties. Finally,we envision that the proposed model can be enhancedto develop a deeper understanding of cooperation inwireless networks by incorporating other parametersthat impact node behavior such as energy consumption.Moreover, as the proposed model is centered aroundgroup interactions, the model can be used to study otherforms of data delivery in wireless networks such asmulti-hop unicast.

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