ExtensiveFormGames2/14/18
Alpha-BetaPruningExercise
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DiscussionQuestions
1. Howcanweorganizethesearchtomaximizetheamountofworksavedbypruning?A. Explorebestnodesfirst(estimatewithheuristic).
2. Howcanwemodifyalpha/betapruningtoworkonnon-zero-sumgames?A. Wecan’t.
3. Howcanwemodifyalpha/betapruningtoworkon3-(ormore)-playergames?A. Wecan’t.
IterativeDeepeninginMin/Max
• Wegenerallyimposeadepthlimitonalpha/betamin/max,basedonhowmuchtimewewanttoallow.
• Ifwehavetimeleftover,wecouldre-runwithalargerdepthlimit. Ifwerunoutoftime,wecanjustreturnthemovefromthelastrun.
Whatcanwemodelsofar?Withminimax,wecansolve:• two-player,zero-sum,completeinformation,sequentialmovegames• lotsofclassicboardgames:chess,checkers,connect4…• notmuchelse,andthesearchspacefortheaboveisoftentoobig
Withbackwardsinduction(sofar)wecansolve:• completeinformation,sequentialmovegames• simplemodelsofeconomiccompetition,afewothereconomicapplications
Gametheoryisn’tjustaboutplayinggames.
• We’dliketomodeldecisionmakinginallsortsofmulti-agentinteractions.
• Todoso,weneedtocomeupwithamodel(suchasagametree)thatdescribestheinteraction.
• Weneedtoidentifytheplayers,whentheymakedecisions,andhowwhattheywanttoachieve.
ExampleApplication:ResourceSharingAlsoknownascake-cutting,asin“Icut,youchoose”.• Oneagentproposesadivisionofadesirableresource,theotheracceptsorrejectsthatdivision.• Here,wemodeltheagentsasgettingutility+1foreachunitofresource,butthey’realsospitefulsotheyfeeladisutilityof0.5iftheyreceivelessthanhalf.• MANYvariationsonthismodelarepossible.
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Whatcan’twemodelsofar?
RandomOutcomes
SimultaneousMoves
IncompleteInformation
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