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hw10 _sp11 - S'11 Prof Stahl ECO 354K Problem Set No 10 Due...

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S'11 Prof. Stahl ECO 354K Problem Set No. 10 Due Friday, April 8 by 5pm Note: Please submit your completed HW to the Econ front desk for the TA . Write “Jonathan Lhost” at the top and have them time stamp it. 1. Consider the following game with payoff uncertainty. The payoff matrix is either A or B: 2) 2) L R . L R . 1) U| 0, 0 | 5,-2 | 1) U| -2, 0 | 5,-2 | D| -2, 7 | 7, 5 | D| 0, 5 | 7, 7 | A B (a) Suppose that at the time they must choose, neither player knows whether payoffs will be given by A or B. After they choose, the matrix will be chosen by a public throw of a die such that the probability of A is 2/3. Find all the sequentially rational Nash equilibria. (b) Suppose the die is thrown before the players choose, but that only player 1 observes the outcome before she chooses; i.e. player 1 knows whether the payoff matrix is A or B, but player 2 only knows that matrix A has a 2/3 chance of being the payoff matrix. Assume that player 2 does not observe player 1's choice before he must choose. Find all the sequentially rational Nash equilibria.
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