ch15 定价的博弈论模型课件.ppt

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1、Chapter15GAMETHEORYMODELSOFPRICING1GameTheoryGametheoryinvolvesthestudyofstrategicsituationsGametheorymodelsattempttoportraycomplexstrategicsituationsinahighlysimplifiedandstylizedsettingabstractfrompersonalandinstitutionaldetailsinordertoarriveatarepresentationofthesituationthatism

2、athematicallytractable2GameTheoryAllgameshavethreeelementsplayersstrategiespayoffsGamesmaybecooperativeornoncooperative3PlayersEachdecision-makerinagameiscalledaplayercanbeanindividual,afirm,anentirenationEachplayerhastheabilitytochooseamongasetofpossibleactionsThespecificidentityof

3、theplayersisirrelevantno“goodguys”or“badguys”4StrategiesEachcourseofactionopentoaplayeriscalledastrategyStrategiescanbeverysimpleorverycomplexeachisassumedtobewell-definedInnoncooperativegames,playersareuncertainaboutthestrategiesusedbyotherplayers5PayoffsThefinalreturnstotheplayers

4、attheendofthegamearecalledpayoffsPayoffsareusuallymeasuredintermsofutilitymonetarypayoffsarealsousedItisassumedthatplayerscanrankthepayoffsassociatedwithagame6NotationWewilldenoteagameGbetweentwoplayers(AandB)byG[SA,SB,UA(a,b),UB(a,b)]whereSA=strategiesavailableforplayerA(aSA)SB=st

5、rategiesavailableforplayerB(bSB)UA=utilityobtainedbyplayerAwhenparticularstrategiesarechosenUB=utilityobtainedbyplayerBwhenparticularstrategiesarechosen7NashEquilibriuminGamesAtmarketequilibrium,noparticipanthasanincentivetochangehisbehaviorIngames,apairofstrategies(a*,b*)isdefined

6、tobeaNashequilibriumifa*isplayerA’sbeststrategywhenplayerBplaysb*,andb*isplayerB’sbeststrategywhenplayerAplaysa*8NashEquilibriuminGamesApairofstrategies(a*,b*)isdefinedtobeaNashequilibriumifUA(a*,b*)UA(a’,b*)foralla’SAUB(a*,b*)Ub(a*,b’)forallb’SB9NashEquilibriuminGamesIfoneofthe

7、playersrevealstheequilibriumstrategyhewilluse,theotherplayercannotbenefitthisisnotthecasewithnonequilibriumstrategiesNoteverygamehasaNashequilibriumpairofstrategiesSomegamesmayhavemultipleequilibria10ADormitoryGameSupposethattherearetwostudentswhomustdecidehowloudlytoplaytheirstereo

8、sinadormeachmaychoo