游戏应用章均衡在任何中每个玩家都会对所参考.pdf

NashEquilibrium

◼InanyNashequilibrium(NE)eachyer

choosesa“best”responsetothechoices

madebyalloftheotheryers.

◼AgamemayhavemorethanoneNE.

◼Howcanwelocateeveryoneofagame’s

Nashequilibria?

◼IfthereismorethanoneNE,canweargue

thatoneismorelikelytooccurthananother?

BestResponses

◼Thinkofa2×2game;i.e.,agamewithtwo

yers,AandB,eachwithtwoactions.

◼AcanchoosweenactionsaAandaA.

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◼BcanchoosweenactionsaBandaB.

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◼Thereare4possibleactionpairs;

(aA1,aB1),(aA1,aB2),(aA2,aB1),(aA2,aB2).

◼Eachactionpairwillusuallycausedifferent

payoffsfortheyers.

BestResponses

◼SupposethatA’sandB’spayoffswhenthe

chosenactionsareaA1andaB1are

AABBAB

U(a1,a1)=6andU(a1,a1)=4.

◼Similarly,supposethat

AABBAB

U(a,a)=3andU(a,a)=5

1212

AABBAB

U(a,a)=4andU(a,a)=3

2121

AABBAB

U(a,a)=5andU(a,a)=7.

2222

BestResponses

AABBAB

◼U(a,a)=6andU(a,a)=4

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