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1、IntroductiontoGameTheoryLecture3NashEquilibriumisaconceptofasteadystateingivensituationNoonecanunilaterallyimprovetheirpayoff,thereforenoonehasincentivetodeviatefromequilibriumactionNashEquilibriumisanactionprofileinwhicheveryplayer’sactionisbestresponsetoeveryotherp
2、layer’sactionNE-ReviewReviewStrict&WeakBestResponseMixedStrategyNESummaryNoplayerwishestochangeherbehavior,knowingtheotherplayers’behavior=>therearenoregretsEquilibriumbehaviorisbasedongeneralknowledgeandexperiencewithsimilarplayersandsituations;notonparticularcircum
3、stancesNE-ReviewReviewStrict&WeakBestResponseMixedStrategyNESummaryWecanfindNashequilibriaby:Eliminationofstrictlydominatedstrategies“CircleMethod”Eliminationmethodissometimesimprecise,NE(CircleMethod,Bestresponses)isstronger.NE-ReviewReviewStrict&WeakBestResponseMix
4、edStrategyNESummaryStrictvsweakdominanceBestresponsefunctions(whycircleswork)MixedstrategiesNashequilibriumPreviewReviewStrict&WeakBestResponseMixedStrategyNESummaryStrictvs.WeakDominanceReviewStrict&WeakBestResponseMixedStrategyNESummaryDefinition:playeri’sactionais
5、trictlydominatesheractionbiifui(ai,a−i)>ui(bi,a−i)foreverylista−ioftheotherplayers’actions,whereuiisapayofffunctionthatrepresentsplayeri’spreferencesDefinition:Ifanyactionstrictlydominatestheactionbi,wesaythatbiisstrictlydominatedStrictDominanceReviewStrict&WeakBestR
6、esponseMixedStrategyNESummaryDefinition:playeri’sactionaiweaklydominatesheractionbiifui(ai,a−i)≥ui(bi,a−i)foreverylista−ioftheotherplayers’actions,whereuiisapayofffunctionthatrepresentsplayeri’spreferencesDefinition:Ifanyactionweaklydominatestheactionbi,wesaythatbiis
7、weaklydominatedWeakDominanceReviewStrict&WeakBestResponseMixedStrategyNESummaryRightstrictlydominatesCenterRightweaklydominatesLeftLeftweaklydominatesCenterStrictvs.WeakDominance2LeftCenterRightUp1,21,10,2Down0,10,12,3ReviewStrict&WeakBestResponseMixedStrategyNESumma
8、ryStrictNE:requiresthattheequilibriumactionisbetterthananyotheraction(giventhatallotherplayerssticktoNEactions)NonstrictNE:requires
