Game Theory in Cooperative Communications
上传者:汪剑锋|上传时间:2015-04-24|密次下载
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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内容需要下载文档才能查看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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内容需要下载文档才能查看 内容需要下载文档才能查看 内容需要下载文档才能查看 内容需要下载文档才能查看 内容需要下载文档才能查看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
4
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
内容需要下载文档才能查看solution.
内容需要下载文档才能查看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
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