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1、DraftchapterfromAnintroductiontogametheorybyMartinJ.Osborne.Version:2002/7/23.Martin.Osborne@utoronto.cahttp://www.economics.utoronto.ca/osborneCopyright©1995–2002byMartinJ.Osborne.Allrightsreserved.Nopartofthisbookmaybere-producedbyanyelectronicormechanicalmeans(i
2、ncludingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromOxfordUniversityPress,exceptthatonecopyofuptosixchaptersmaybemadebyanyindividualforprivatestudy.2NashEquilibrium:Theory2.1Strategicgames112.2Example:thePrisoner'sDilemma12
3、2.3Example:BachorStravinsky?162.4Example:MatchingPennies172.5Example:theStagHunt182.6Nashequilibrium192.7ExamplesofNashequilibrium242.8Bestresponsefunctions332.9Dominatedactions432.10Equilibriuminasinglepopulation:symmetricgamesandsymmetricequilibria49Prerequisite:
4、Chapter1.2.1StrategicgamesASTRATEGICGAMEisamodelofinteractingdecision-makers.Inrecognitionoftheinteraction,werefertothedecision-makersasplayers.Eachplayerhasasetofpossibleactions.Themodelcapturesinteractionbetweentheplayersbyallowingeachplayertobeaffectedbytheactio
5、nsofallplayers,notonlyherownaction.Specically,eachplayerhaspreferencesabouttheactionprole—thelistofalltheplayers'actions.(SeeSection17.4,inthemathematicalappendix,foradiscussionofproles.)Moreprecisely,astrategicgameisdenedasfollows.(Thequalication“withordinalp
6、references”distinguishesthisnotionofastrategicgamefromamoregeneralnotionstudiedinChapter4.)IDEFINITION11.1(Strategicgamewithordinalpreferences)Astrategicgame(withordinalpreferences)consistsof•asetofplayers•foreachplayer,asetofactions•foreachplayer,preferencesoverth
7、esetofactionproles.1112Chapter2.NashEquilibrium:TheoryAverywiderangeofsituationsmaybemodeledasstrategicgames.Forexam-ple,theplayersmayberms,theactionsprices,andthepreferencesareectionoftherms'prots.Ortheplayersmaybecandidatesforpoliticalofce,theactionscampaig
8、nexpenditures,andthepreferencesareectionofthecandidates'proba-bilitiesofwinning.Ortheplayersmaybeanimalsghtingoversomeprey,theac-tionsconcessio
