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1、Twoequivalenceresultsfortwo-personstrictgamesPingzhongTang,FangzhenLinAbstractAgameisstrictifforbothplayers,differentprofileshavedifferentpayoffs.Twogamesarebestresponseequivalentiftheirbestresponsefunctionsarethesame.Weprovethatatwo-personstrictgamehasatmostonepureNashequilibriumifandonlyifitisbe
2、stresponseequivalenttoastrictlycompetitivegame,andthatitisbestresponseequivalenttoanordinalpotentialgameifandonlyifitisbestresponseequivalenttoaquasi-supermodulargame.Keywords:Strictlycompetitivegames；Ordinalpotentialgames；Quasi-supermodulargames；Bestresponseequivalence；Strictgames朗读Yóuxìjíshìyáng
3、éde,rúguǒduìliǎngmíngqiúyuán,bùtóngcèmiànyǒubùtóngdehuíbào.Liǎngchǎngbǐsàishìzuìhǎodehuídáděngjiàde,rúguǒtāmendezuìjiāfǎnyìnghánshùshìxiāngtóngde.Wǒmenzhèngmíngliǎoyīliǎnggèrénzàizuìyángédeyóuxìyīgèchúnnàshénjūnhéngde,dāngqiějǐndāngtāshìzuìhǎodehuídáxiāngdāngyúyīgèyángédejìngzhēngyóuxì,zhèshìzuìhǎ
4、odehuídáxiāngdāngyúyīgèxùqiánzàideyóuxì,dāngqiějǐndāngtāshìzuìhǎodeFǎnyìngxiāngdāngyúyīgèzhǔnchāomóyóuxì字典-查看字典详细内容1.IntroductionInthispaperweprovetworesultsaboutpureNashequilibria(PNEs)for2-personstrictgames,whicharethosewherepayofffunctionsareone-to-one.Thefirstresultsaysthata2-personstrictgameh
5、asatmostonePNEifitisbest-responseequivalent(Rosenthal,1974)toastrictlycompetitivegame(Moulin,1976;Friedman,1983).Thesecondresultsaysthata2-personstrictgameisbest-responseequivalenttoanordinalpotentialgame(MondererandShapley,1996)ifitisbest-responseequivalenttoaquasi-supermodulargame(Topkis,1998).T
6、heseresultscameoutofourprojectonusingcomputerstodiscovertheoremsingametheory(see,e.g.TangandLin,2009).WewerelookingforconditionsthatimplytheuniquenessandexistenceofthePNEs,andwereusingcomputerstorunthroughalargesetofconjectures.Giventhenumberofallpossiblegames,itmadesensetotesttheseconditionsfirst
7、onsomespecialclassesofgames,andtheclassofstrictgamesisanaturalchoiceasinthesegames,thepayofffunctionsareone-to-one,thuseasiertogenerate.Asitturnedout,someinterestingconditionsholdonlyforthisclassofgames.Wehavedes
