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1、SolutionConcept:SequentialEquilibriaofExtensive-FormGames(I)-111.MixedStrategiesandBehaviouralStrategies1.1Review:what’stheextensiveformgamelike?2tee2,-21.a2.0MRaisedFoP1,-1reldas1,-1s.5000.5teble-2,2aMck1.braise2.0foldPa1,-1-1,1ssFigure2:ACardGameEachdecisionnodehastwolabels.T
2、otheleftofthedecimalpoint,itistheplayerlabel.Totherightofthedecimalpoint,itistheinformationlabel,whichisalsocalledinformationstate.3eGExtensive-formgames.NThesetofplayers.SThesetofallpossibleinformationstatesforiplayeriinNofthegameGe.Sa={1.,1.}bS={2.0}12tee2,-21.a2.0MRaiseedFol
3、dPas1,-1Figure1:Ar1,-1s.5CardGame000.5teble-2,2aMck1.braise2.0foldPa1,-1-1,1ss4Assumethatplayers’informationstatesaredisjointsetsSS∩=∅,forij≠.ijTheunionofalltheinformationsets.**SSS=∪.iNi∈*Sa=∪{1.,1.}b{2.0}.5Inagameofperfectinformation,eachinformationset(orstate)containsexactly
4、onedecisionnode.6ThesetofnodesbelongtoplayeriwithinformationYsstates.Thesetofallmove-labelsofalternativebranchesDsfollowinganynodeinY.stee2,-21.a2.0MRaiseedPa1,-1rF1,-1sso.5ld000.5teble-2,2aMck1.braise2.0Pass1,-1fold-1,1Figure1:ACardGame7Apureafunctionthatspecifiesamoveforthepa
5、yeratstrategyeachofhispossibleinformationstateinthegameCThesetofpurestrategiesforplayeri.iCD=×.is∈Ssitee2,-21.a2.0MRaiseedPas1,-1Figure1:ArF1,-1s.5oldCardGame000.5teble-2,2aMck1.braise2.0fPa1,-1old-1,1ss81.2Arandomised-strategyprofile,amixedstrategyprofileandabehaviouralstrateg
6、yprofile?9Therearetwodifferentwaysofrepresentinganextensive-formgamebyastrategic-formgame:Thenormalrepresentation,andthemultiagentrepresentation.Hence,therearetwodifferentwaystodefinerandomizedstrategyprofilesforanygivenextensive-formgameGe.Amixedstrategyprofileandabehaviourals
7、trategyprofile.10anyrandomised-strategyprofileforthenormalrepresentationofGe.Amixed-strategyprofilespecifies,foreachplayer,aprobabilityofGedistributionoverhissetofoverallstrategies.×Δ()Cthesetofmixed-strategyprofilesofGe.iN∈i11anyrandomised-strategyprofileforthemultiagentrepres
8、entationofGe.Abehavioural-strategyprofileofspecifiesap
