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ID:31627111
大小:1.85 MB
页数:150页
时间:2019-01-16
《[博弈论书籍].computational.game.theory,yishay mansour,2003》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、ComputationalLearningTheorySpringSemester,2003/4Lecture1:March2Lecturer:YishayMansourScribe:GurYaari,IdanSzpektor1.1IntroductionSeveralfieldsincomputerscienceandeconomicsarefocusedontheanalysisofGametheory.UsuallytheyobserveGameTheoryasawaytosolveoptimizatio
2、nproblemsinsystemswheretheparticipantsactindependentlyandtheirdecisionsaffectthewholesystem.FollowingisalistofresearchfieldsthatutilizeGameTheory:•ArtificialIntelligence(AI)-MultipleAgentssettingswheretheproblemisusuallyacooperationproblemratherthanacompetitio
3、nproblem.•CommunicationNetworks-Distributionofworkwhereeachagentworksindepen-dantly.•ComputerScienceTheory-ThereareseveralsubfieldsthatuseGameTheory:–Maximizingprofitinbidding–Minimumpenaltywhenusingdistributionalenvironment–Complexity–Behavioroflargesystems1
4、.2CourseSyllabus•BasicdefinitionsinGameTheory,concentratingonNashEquilibrium•CoordinationRatio–ComparisonbetweenglobaloptimumandNashEquilibrium–LoadBalancingModels•ComputationofNashEquilibrium–ZeroSumgames(LinearProgramming)–ExistenceofNashEquilibriumingener
5、algames12Lecture1:March2•Regret-playingan“unknown”game.Optimizingaplayer’smoveswhentheplayercanonlyviewherownpayoff•VectorPayoff-thePayofffunctionisavectorandthetargetistoreachaspecifictargetset•CongestionandPotentialgames-gamesthatmodelastateofload•Convergence
6、intoEquilibrium•Other...1.3StrategicGamesAstrategicgameisamodelfordecisionmakingwherethereareNplayers,eachonechoosinganaction.Aplayer’sactionischosenjustonceandcannotbechangedafterwards.EachplayericanchooseanactionaifromasetofactionsAi.letAbethesetofallposs
7、ibleactionvectors×j∈NAj.Thus,theoutcomeofthegameisanactionvector~a∈A.Allthepossibleoutcomesofthegameareknowntoalltheplayersandeachplayerihasapreferencerelationoverthedifferentoutcomesofthegame:~ai~bforevery~a,~b∈A.Therelationstandsiftheplayerprefers~bover~a
8、,orhasequalpreferenceforeither.DefinitionAStrategicGameisatriplethN,(Ai),(i)iwhereNisthenumberofplayers,Aiisthefinitesetofactionsforplayeriandiisthepreferencerelationofplayeri.Wewilluseaslightlydifferen
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