國外博弈論課件lecture(9)-資料下載頁
2024-10-19 13:59本頁面
【正文】 prefers the prize fight. Pat Opera Prize Fight Chris Opera 2 , 1 0 , 0 Prize Fight 0 , 0 1 , 2 June 20, 2021 73347 Game TheoryLecture 23 21 Battle of the sexes with inplete information (version one) ? Now Pat’s preference depends on whether he is happy. ? If he is happy then his preference is the same. ? If he is unhappy then he prefers to spend the evening by himself and his preference is shown in the following table. ? Chris cannot figure out whether Pat is happy or not. But Chris believes that Pat is happy with probability and unhappy with probability Payoffs if Pat is unhappy Pat Opera Prize Fight Chris Opera 2 , 0 0 , 2 Prize Fight 0 , 1 1 , 0 June 20, 2021 73347 Game TheoryLecture 23 22 Battle of the sexes with inplete information (version one) cont’d ? How to find a solution ? Payoffs if Pat is unhappy with probability Pat Opera Prize Fight Chris Opera 2 , 0 0 , 2 Prize Fight 0 , 1 1 , 0 Payoffs if Pat is happy with probability Pat Opera Prize Fight Chris Opera 2 , 1 0 , 0 Prize Fight 0 , 0 1 , 2 June 20, 2021 73347 Game TheoryLecture 23 23 Battle of the sexes with inplete information (version one) cont’d ? Best response ? If Chris chooses opera then Pat’s best response: opera if he is happy, and prize fight if he is unhappy ? Suppose that Pat chooses opera if he is happy, and prize fight if he is unhappy. What is Chris’ best response? ? If Chris chooses opera then she get a payoff 2 if Pat is happy, or 0 if Pat is unhappy. Her expected payoff is 2?+ 0?=1 ? If Chris chooses prize fight then she get a payoff 0 if Pat is happy, or 1 if Pat is unhappy. Her expected payoff is 0?+ 1?= ? Since 1, Chris’ best response is opera ? A Bayesian Nash equilibrium: (opera, (opera if happy and prize fight if unhappy)) June 20, 2021 73347 Game TheoryLecture 23 24 Battle of the sexes with inplete information (version one) cont’d ? Best response ? If Chris chooses prize fight then Pat’s best response: prize fight if he is happy, and opera if he is unhappy ? Suppose that Pat chooses prize fight if he is happy, and opera if he is unhappy. What is Chris’ best response? ? If Chris chooses opera then she get a payoff 0 if Pat is happy, or 2 if Pat is unhappy. Her expected payoff is 0?+ 2?=1 ? If Chris chooses prize fight then she get a payoff 1 if Pat is happy, or 0 if Pat is unhappy. Her expected payoff is 1?+ 0?= ? Since 1, Chris’ best response is opera ? (prize fight, (prize fight if happy and opera if unhappy)) is not a Bayesian Nash equilibrium. June 20, 2021 73347 Game TheoryLecture 23 25 Summary ? Cournot duopoly model of inplete information (version two) ? Battle of the sexes with inplete information (version one) ? Next time ? Bayesian Nash equilibrium ? Reading lists ? Chapter of Gibbons
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