Cluster Consensus on Networks with Diversified Interactions

Game and Evolutionary Game in Communication NetworksYuedong Xu2013.12.04OutlineGame Theory: A Premier

Evolutionary Game

Applications to Networks

Potential Research FieldsUsing as less math as possible !Game Theory: A PremierWhat is game about?

Game of Chickendriver who swerves away looses

What should drivers do?To swerve or to stay?

223Game Theory: A PremierWhat is game about?

Game of Chickendriver who swerves away looses

22swervestayswerve0, 0-1, 5stay5, -1-10, -10Driver 1Driver 2Drivers want to do opposite of one another4Game Theory: A PremierA Game consists ofat least two players a set of strategies for each playera payoff for each strategy profileBasic assumption (rationality of players)Nash Equilibriumno player can improve its payoff by unilaterally changing its strategyPareto optimality, price of anarchyGame Theory: A PremierNon-Cooperative (Competitive) Gamesindividualized play

Cooperative Gamesplay as a group

Repeated, Stochastic and Evolutionary Gamesnot one shotClassification 1:Game Theory: A PremierClassification 2:Non-cooperativeCooperativeStaticDynamic (repeated)Strategic-formExtensive-formPerfect informationImperfect informationComplete informationIncomplete informationGame Theory: A PremierInternet ApplicationSelfish Routing gamesvwtC(x) = 1C(x) = xC(x) = 1C(x) = xC(x) = 0Game Theory: A PremierInternet Application

P2P Networks: Bittorrent, Xunlei, Pplive, PPStream, QQLive Game Theory: A PremierInternet Application

Internet Ecosystem (Business Models)Game Theory: A PremierInternet ApplicationCloud Computing game

Game Theory: A PremierInternet ApplicationOnline Social Networks

Game Theory: A PremierInternet ApplicationNetwork Security Game

Game Theory: A PremierWireless Application802.11 multiple access game

Game Theory: A PremierWireless Application3G/4G Power Control Game

Game Theory: A PremierWireless ApplicationPacket forwarding game??BlueGreenGame Theory: A PremierWireless ApplicationCognitive radio network game

Game Theory: A PremierWireless ApplicationWireless jamming and eavesdrop games

EOutlineGame Theory: A Premier

Evolutionary Game

Applications to Networks

Potential Research FieldsRecapFollow the crowd! Evolutionary game theoryEvolutionary game theory (EGT)

refinement of CGTgame in a populationdynamics of strategy adoptionmutual learning among playersEvolutionary game theory differs from classical game theory by focusing more on the dynamics of strategy change as influenced not solely by the quality of various competing strategies, but by the effect of frequency with which the various competing strategies are found in the population. Evolutionary game theoryEvolutionary game theory (EGT)Usually two types of game: games against the field and games with pairwise contests

A game against the eld is one in which there is no specic opponentfor a given individual - their payoff depends on what everyone in thepopulation is doing. Ex: Choice of GenderA pairwise contest game describes a situation in which a givenindividual plays against an opponent that has been randomly selected(by nature) from the population and the payoff depends just on whatboth individual do. Ex: Hawk-Dove GameEvolutionary game theoryA profile of evolutionary game

Payoff (fitness)Evolutionary game theoryEvolutionary stable strategy (ESS)

Theorem (ESS)An evolutionarily stable strategy is a strategy which, if adopted by a population of players, cannot be invaded (or replaced) by any alternative strategy that is initially rare.

Evolutionary game theory

Evolutionary game theoryExample (Hawk-Dove Game) contIn the population, the payoff of a mutant is

Evolutionary game theory

Evolutionary game theoryEvolutionary game theoryLyapunov stability vs asymptotic stabilityLyapunov function and Engenvalue approachEvolutionary game theoryESS vs NE in associated two-player game

An ESS is a (mixed) NE A NE might not be an ESSAsymmetric NE in monomorphic populationUnstable NE

Evolutionary game theoryReplicator dynamics and NEIn a two-strategy gameAny NE is a fixed point of replicator dynamicsNot every fixed point corresponds to a NEReplicator dynamics and ESSESS is an asymptotically stable fixed pointTwo strategy pair-wise contest

More than two strategies OutlineGame Theory: A Premier

Evolutionary Game

Applications to Networks

Potential Research FieldsPeer-to-peer file sharingWireless networksPeer-to-peer file sharingFile Piece (e.g. chunk, block)A content is split in piecesEach piece can be independently downloadedLeecherA peer that is client and serverIn the context of content deliveryHas a partial copy of the contentSeedA peer that is only serverIn the context of content deliveryHas a full copy of the content

Great improvement over customer-server modeIdeal system: single chunk, fully cooperativeBig System: many peers, many chunks, stochastic system

timet=0t=Tt=2T

Seed34Peer-to-peer file sharingWhich peers shall I serve in each time slot?34Peer-to-peer file sharingIf no good incentive strategySlow serviceEven overwhelmed by requests

Incentive modelA strategy is the behavior (providing/rejecting a service) of a peer against other peersA policy is the set of rules of for incentivizationA point is a utility measure of peersA system is robust : convergence and cooperation

Q. Zhao, J. Lui, D. ChiuA Mathematical Framework for Analyzing Adaptive Incentive Protocols in P2P Networks, IEEE/ACM Trans. Networking, 2012Peer-to-peer file sharingIncentive model (cont)Strategy = type of peerFinite strategies {cooperator, defector, reciprocator}

Always serveAlways rejectServe cooperators and reciprocators with certain probabilities,reject defectorsPeer-to-peer file sharingIncentive model (cont)System description:

Incentive scheme (esp. for reciprocators)

At the beginning of each time slot, each peer randomly selects another peer to request for service. The selected peer chooses to serve the request based on his current strategy. A peer obtains points if its request is served and loses (=1) points if it provides service to others.Peer-to-peer file sharingUtility modelAfter a long way, the points gained by a type-i peer

We can now studyequilibrium state (given G)is the equilibrium stable?how to reach this equilibrium?how good is the incentive scheme

Type-i payoffNetwork payoffIs this enough?

Peer-to-peer file sharingLearning model in P2P networksCurrent best learning model

At the end of each slot, a peer chooses to switch to another strategy s with certain prob. To decide which strategy to choose, the peer learns from other peers.Needs to compute the gains of all other peers !Peer-to-peer file sharingLearning model in P2P networksOpportunistic learning model

At the end of each slot, each peer chooses another peer as its teacher with certain prob. If the teacher is of a different type and performs better, this peer adapts to the teachers strategy with another prob. Simpler !Peer-to-peer file sharingNow we can studyRobustness of incentive scheme

Mirror incentive policyreciprocators are tit-for-tatProportional incentive policyA reciprocators always serves any other reciprocatorLinear incentive policy

Each scheme generates a different matrix G !Prob. That reciprocators serve other types of peers! Peer-to-peer file sharing

Peer-to-peer file sharingIn relation to EGpair-wise contest population gamepeers players; chunk exchange2 players games

Opp. LearningAfter some effortsReplicator dynamicsCurr. Best LearningLarge-scale wireless networks

Random multiple access (slotted ALOHA)A node transmits with prob. p in each slotSimultaneous transmission collisionsLarge-scale wireless networksPower control game (signal to noise interference ratio, SINR)

Large power better throughputLarge power more interference to other receiversLarge-scale wireless networksLarge-scale wireless networksSad facts:Selfishness is unsuccessfulOptimal cooperation is hard in a large distributed networks (bargaining, Shapley value)

Evolutionary game kicks in!

H. Tembine, E. Altman, Evolutionary Games in Wireless Networks, IEEE Trans. Syst. Man Cyber. B, 2010What if wireless nodes learn from each other in local interactions?Large-scale wireless networksChallengesStandard EGT: a player interacts with all other players (or average population)Large-scale wireless networks: no longer strategic pair-wise competitionrandom number of local playersnon-reciprocal interactionsFinite strategies of a player {transmit, stay quiet} in multiple access game {high power, low power} in power control game

Non standard EGT Standard EGTLarge-scale wireless networksWCDMA power control gameSINR with distance r between transmitter and receiver of node i is given by

PHPLPH

Pi : the strategy of node i (i.e., PH or PL)x : the proportion of the population choosing PHg : channel gain, r0 is the radius-of-reception circle of receiver : the attenuation order with value between 3 and 6, : the noise power, and : the inverse of processing gainI(x) : total interference from all nodes to the receiver of node iLarge-scale wireless networksWCDMA power control gamePayoff of node i is as follows:

R : transmission rangewp : cost weight due to adopting power Pi (e.g. energy consumption)(r) : probability density function given the density of receiver Large-scale wireless networksWCDMA power control gameExistence of uniqueness of ESSReplicator dynamics

This function is continuous and strictly monotonic, which is required for the proof of stability based on sufficient conditionLarge-scale wireless networksSome other related worksExtensions to EGT

Applications P. Coucheney, C. Touati. Fair and Efficient User-Network Association Algorithm for Multi-Technology Wireless Networks, IEEE Infocom 2009 (mini)S. Shakkottai, E. Altman. The Case for Non-cooperative Multihoming of Users to Access Points in IEEE 802.11 WLANs, IEEE Infocom 2006C. Jiang, K. Liu, Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View, IEEE Trans. Signal Processing, 2013E. Altman, Y. Hayel. Markov Decision Evolutionary Games, IEEE Trans. Auto. Ctrl. 2010X. Luo and H. Tembine. Evolutionary Coalitional Games for Random Access Control, IEEE Infocom 2013 (mini)Large-scale wireless networksSummaryP2P : practical problem EG theoryWCDMA: EG theory practical problem

Common Challenges:difficult to find important problemdifficult to have theoretical contributions to EGT

Two different styles !Thank you!

Q & A