博弈论英文课件-(3).pdf

Static(orSimultaneous-

Move)GamesofComplete

Information

Matchingpennies

Player2

HeadTail

Head-1,11,-1

Player1

Tail1,-1-1,1

nHeadisPlayer1’sbestresponsetoPlayer2’sstrategyTail

nTailisPlayer2’sbestresponsetoPlayer1’sstrategyTail

nTailisPlayer1’sbestresponsetoPlayer2’sstrategyHead

nHeadisPlayer2’sbestresponsetoPlayer1’sstrategyHead

ØHence,NONashequilibrium

Solvingmatchingpennies

Player2

HeadTail

Head-1,11,-1r

Player1

Tail1,-1-1,11-r

q1-q

nRandomizeyourstrategies

ØPlayer1choosesHeadandTailwithprobabilitiesrand

1-r,respectively.

ØPlayer2choosesHeadandTailwithprobabilitiesqand

1-q,respectively.

nMixedStrategy:

ØSpecifiesthatanactualmovebechosenrandomlyfromthe

setofpurestrategieswithsomespecificprobabilities.

Mixedstrategy

nAmixedstrategyofaplayerisaprobability

distributionoverplayer’s(pure)strategies.

ØAmixedstrategyforChrisisaprobabilitydistribution(p,

1-p),wherepistheprobabilityofplayingOpera,and1-

pisthatprobabilityofplayingPrizeFight.

ØIfp1thenChrisactuallyplaysOpera.Ifp0then

ChrisactuallyplaysPrizeFight.

BattleofsexesPat

OperaPrizeFight

Opera(p)2,1