Game Theory in Cooperative Communications

Game Theory in Cooperative Communications 博弈论 协作通信

GameTheoryinCooperativeCommunications

DejunYang,XiFang,andGuoliangXue

Abstract

Cooperativecommunicationhasgreatpotentialtoimprovethewirelesschannelcapacitybyexploitingtheantennasonwirelessdevicesforspatialdiversity.However,applicationsofcooperativecommunicationarebarelyseeninreality.Amainobstacleblockingitswideapplicationsisthelackofincentivesforwirelessnodestoparticipateincooperativecommunication.We?rstsurveytheexistinggametheoreticsolutionsforprovidingcooperationincentivesincooperativecommunications.Wethendiscussthechallengesinapplyinggametheorytocooperativecommunications.

Keywords:

I.INTRODUCTION

Cooperativecommunicationhasbeenproposedtoimprovethechannelcapacityinwirelessnetworks.Ittakesadvantageofthebroadcastnatureofwirelesstransmissionandutilizestheantennasonwirelessnodestoachievespacialdiversity.Dependingonhowtherelaynodeprocessestheoverheardsignal,twoprimarycooperativecommunicationmodesarewidelyused:Amplify-and-Forward(AF)andDecode-and-Forward(DF).IntheAFmode,therelaynodeampli?esthesignalbeforeforwardingittothedestinationnode.IntheDFmode,therelaynodedecodesandencodesthesignalbeforeforwardingittothedestinationnode.Cooperativecommunicationhaspotentialapplicationsinmanydifferentnetworks,includingcellularnetworks,ad-hocnetworks,andcognitivenetworks,asshowninFig.1.

Toachievecooperativecommunication,cooperationfromothernodesisrequired.Innetworkapplicationsformilitaryactionsanddisasterrelief,cooperationamongnodescanbeassumedsincethenodesbelongtoasingleauthorityandthusvoluntarilycooperatetoachieveacommongoal.However,incommercialapplications,wherenodesusuallybelongtodifferentindependententities,thereisnogoodreasontoassumethatthenodeswillcooperate.Infact,nodesaresel?shandconsumetheirresourcesonlywhendoingsocanmaximizetheirownbene?ts.GametheoryAllauthorsareaf?liatedwithArizonaStateUniversity,Tempe,AZ85287.E-mail:{dejun.yang,xi.fang,xue}@asu.edu.ThisresearchwassupportedinpartbyNSFgrants0905603and1115129.Theinformationreportedheredoesnotre?ectthepositionorthepolicyofthefederalgovernment.

Game Theory in Cooperative Communications 博弈论 协作通信

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appropriatetooltomodel,analyzeandsolvetheproblemsincooperativecommunications.

(a)Cellularnetwork

Fig.1.(b)Ad-hocNetwork(c)CognitiveRadioNetworkNetworkswherecooperationcommunicationcanbeapplied

Gametheoryisthestudythatanalyzesthestrategicinteractionsamongmakers,whoseactionshavemutual,probablycon?icting,consequences.Originallydevelopedtomodelproblemsinthe?eldofeconomics,gametheoryhasrecentlybeenappliedtonetworkproblems,toThereasonthatgametheoryisanappropriatechoiceforstudyingcooperativecommunicationsismultifold.First,nodesinthenetworkareautonomousagents,makingdecisionsonlyfortheirowninterests.Gametheoryprovidesussuf?cienttheoreticaltoolstoanalyzethenetworkusers’behaviorsandactions.Second,gametheoryprimarilydealswithdistributedoptimization,whichoftenrequireslocalinformationonly.Thusitenablesustodesigndistributedalgorithms.Finally,auction,amarketgameofincompleteinformation,allowsustodesignmechanismswhererelaynodescanselltheirresourcestothesourcenodesforcooperativecommunications.Suchapproachisdesirablewhenneitherthesourcenodenortherelaynodeknowseachother’sprivatevaluationontheresourcestotrade.

Inthefollowingsections,we?rstintroducethebasicconceptsofcooperativecommunicationandgametheory.Wethensurveytheexistinggametheoreticsolutionstocooperativecommu-nicationproblems,withthefocusoncooperationincentiveprovisioning.Finally,wediscusstheresearchchallengesinapplyinggametheorytotheproblemsincooperativecommunications.

II.COOPERATIVECOMMUNICATION

Dependingontheavailabilityofnodesandthecooperativecommunicationprotocols,therearethreedifferentcommunicationtopologies:one-to-one,one-to-many,andmany-to-one,asshown

Game Theory in Cooperative Communications 博弈论 协作通信

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thesimplesttopology,one-to-one,asanexampletoillustratethebasicideaofcooperativecommunication.Inthisexample,??isthesourcenodethattransmitsinformation,??isthedestinationnodethatreceivesinformation,and??istherelaynodethatrelaysinformationtoenhancethecommunicationbetweenthesourceandthedestination.Let????and????denotethetransmissionpowerof??and??,respectively.Let??denotethebandwidthofthetransmissionchannel.Assumethattransmissionproceedsinaframe-by-framefashion,asshowninFig.3.Eachframeisdividedintotwophases.Inthe?rstphase,thesourcenode??transmitsitsdatatothedestinationnode??.Duetothebroadcastnatureofwirelesstransmission,therelaynode??canoverhearthedata.Inthesecondphase,therelaynode??forwardsthedatatothedestination??afterprocessing,dependingontheunderlyingcooperativecommunicationmode.

(a)One-to-one

Fig.2.Threecooperativecommunicationtopologies(b)One-to-many(c)Many-to-one

Fig.3.Illustrationofcooperativecommunication

Wenextcomputetheachievablecapacityundercooperativecommunications[1].Whennode??transmitsasignaltonode??withpower????,thesignal-to-noiseratio(SNR)atnode??,denotedby??????????,is

??????????=????,??0?∣∣??,??∣∣??

where??0istheabientnoise,∣∣??,??∣∣istheEuclideandistancebetweennodes??and??,and??isthepathlossexponentwhichisbetween2and4ingeneral,dependingonthecharacteristicsofthecommunicationmedium.

Game Theory in Cooperative Communications 博弈论 协作通信

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Amplify-and-Forward(AF):Intheamplify-and-forwardmode,therelaynodeampli?esthesignaltransmittedbythesourcenodeinthe?rsttimeslotandthentransmitstheampli?edsignaltothedestinationnodeinthesecondtimeslot.Theachievablecapacityfrom??to??is()???????????????????????log21+??????????+.??????(??,??,????,??)=2??????????+??????????+1

Decode-and-Forward(DF):Inthedecode-and-forwardmode,therelaynodedecodesandestimatesthesignaltransmittedbythesourcenodeinthe?rsttimeslotandthentransmitsthedatatothedestinationnodeinthesecondtimeslot.Theachievablecapacityfrom??to??is

?? ??(??,??,????,??)=??min{log2(1+??????????),log2(1+??????????+??????????)}.2

III.GAMETHEORYBASICSINANUTSHELL

Gametheory[2]isadisciplineaimedatmodelingscenarioswhereindividualdecision-makershavetochoosespeci?cactionsthathavemutualorpossiblycon?ictconsequences.Agameconsistsofthreemajorcomponents:

?

?players:Thedecisionmakersarecalledplayers,denotedbya?niteset??={1,2,...,??}.strategy:Eachplayer??∈??hasanon-emptystrategyset????.Let????denotetheselectedstrategybyplayer??.Astrategypro?le??consistsofallplayers’strategies,i.e.,??=(??1,??2,...,????).Obviously,wehave??∈??=×??∈??????,where×istheCartesianproduct.

utility/payoff:Theutilityofplayer??isameasurementfunction,denotedby????:??→?,onthepossibleoutcomedeterminedbythestrategiesofallplayers,where?isthesetofrealnumbers.?

ThemappingfromthecomponentsinagametotheelementsincooperativecommunicationsisshowninTableI.

Theplayersofthegameareassumedtoberationalandsel?sh,whichmeanseachplayerisonlyinterestedinmaximizingitsownutilitywithoutrespectingothers’andthesystem’sperformance.Let?????denotethestrategypro?leexcluding????.Asanotationalconvention,wehave??=(????,?????).Wesaythatplayer??prefers????to??′??if????(????,?????)>????(??′??,?????).Whenotherplayers’strategiesare?xed,player??canselectastrategy,denotedby????(?????),whichmaximizesitsutilityfunction.Suchastrategyiscalledabestresponseofplayer??.Astrategyiscalledadominantstrategyofplayer??if,regardlessofwhatotherplayersdo,thestrategyearnsplayer??alargerutility

Game Theory in Cooperative Communications 博弈论 协作通信

Not Cooperate2, 53, 3

TABLEI

COMPONENTSOFGAMESINCOOPERATIVECOMMUNICATIONS5ComponentsintheGame

Players

StrategyElementsinCooperativeCommunicationsSourcenodesand/orrelaynodesPowercontrol[3–7]

Spectrumallocation[8]

Relaynode(s)orsourcenode(s)selection[9]

Tocooperateornot[10]

Price[3,9,11,12]

Utility/PayoffDatarate[6,10]

Pro?t,e.g.,revenueminuscost[3–5,7–9,11]

thananyotherstrategy.Inordertostudytheinteractionsamongplayers,theconceptofNashEquilibrium(NE)isintroduced.strategypro?leconstitutesanNEifnoneoftheplayerscanimproveitsutilitybyunilaterallydeviatingfromitscurrentstrategy.Tocharacterizeandquantifytheinef?ciencyofthesystemperformanceduetothelackofcooperationamongtheplayers,weusetheconceptofofanarchy(POA).ThePOAofthegameistheratioofthesystemperformanceintheworstNEtothesystemperformanceinthesocialoptimal

solution.

Fig.4.Two-playercooperativecommunication

Toillustratethebasicconceptsofgametheory,weuseasimpletwo-playerexample.Thisgameisessentiallyequivalenttothewell-studiedgame,Dilemma.Therearetwoplayersinthisgame,player1andplayer2.Eachplayercanchoosefromtwostrategies,Cooperate(C)andNotCooperate(NC).Ifplayer1takesstrategyC,itwillactasarelayforplayer2forcooperativecommunication.Otherwise,player1onlytransmitsitsowndatatothedestination.Thereforetherearetotallyfourdifferentstrategypro?les.Theutilitiesofdifferentpro?lesareshowninthetableinFig.4.Itisstraightforwardtoseethat(NC,NC)isanNEwithsocial