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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