PS3solutions

PS3solutions - Econ 171 Spring 2010 Problem Set 3 -...

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Econ 171 Spring 2010 Problem Set 3 - Solutions Due Tuesday, June 1 Important: hand in only the two-star problems. There are no one-star problems on this problem set. The notation a.b denotes problem number b from Chapter a in Watson. ** Problem 1 Consider a two-player Bayesian game where both players are not sure whether they are playing the game X or game Y , and they both think that the two games are equally likely. L M R T 1 ,. 2 1 , 0 1 ,. 3 B 2 , 2 0 , 0 0 , 3 X L M R T 1 ,. 2 1 ,. 3 1 , 0 B 2 , 2 0 , 3 0 , 0 Y (a) This game has a unique Bayesian Nash equilibrium, which involves only pure strategies. What is it? (Hint: start by looking for Player 2’s best response to each of Player 1’s actions.) Solution: The unique BNE is ( B,L ), yielding each player a payoff of 2. Player 1’s payoffs do not depend upon which version of the game is actually being played. Her best response to L is to play B and T is a best response to M or R . If 1 plays T , then both M and R give Player 2 an expected utility of . 15, so her best response is L . Similarly, Player 2’s best response to B is L . So in expected utility, L is a dominant strategy for 2, and 1 best responds with B . (b) Now consider a variant of this game in which Player 2 knows which game is being played (but Player 1 still does not). This game also has a unique Bayesian Nash equilibrium. What is it? (Hint: Player 2’s strategy must specify what she chooses
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PS3solutions - Econ 171 Spring 2010 Problem Set 3 -...

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