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slide27-nov7 - ECON 401: Game theory: Bayes Nash...

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ECON 401: Game theory: Bayes Nash Equilibrium Siyang Xiong Rice University November 11, 2011 Xiong (Rice University) ECON 401 November 11, 2011 1 / 6
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Bayesian Nash Equilibrium Suppose players are not exactly sure of their payo/s. player 1 observes a signal 1 , which partially determines the payo/s. player 2 observes a signal 2 , which partially determines the payo/s. For example: 1 , 2 2 f 0 , 1 g , and there is a common prior (distribution) on v 1 , v 2 : v 2 D 0 v 2 D 1 1 D 0 0 1 4 v 1 D 1 1 2 1 4 Xiong (Rice University) ECON 401 November 11, 2011 2 ± 6
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Bayesian Nash Equilibrium 1 D 0 , 2 D 0 C D A 3 , 3 0 , 0 B 0 , 0 3 , 3 1 D 0 , 2 D 1 C D A 3 , 3 3 , 0 B 3 , 3 3 , 3 1 D 1 , 2 D 0 C D A 3 , 3 0 , 3 B 2 , 3 3 , 3 1 D 1 , 2 D 1 C D A 3 , 0 0 , 3 B 0 , 4 1 , 0 Xiong (Rice University) ECON 401 November 11, 2011 3 / 6
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Bayesian Nash Equilibrium after observing the signal, each play forms a posterior belief on his v 2 D 0 v 2 D 1 1 D 0 0 1 4 v 1 D 1
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slide27-nov7 - ECON 401: Game theory: Bayes Nash...

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