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Unformatted text preview: Problem Set 4. Ben Polak Econ 159a/MGT522a Three questions due October 10, 2007 (1) Comparative Statics of Mixed Strategy Equilibria. Consider the following twoplayer game. l r U 12 ; 2 3 ; 9 D 5 ; 8 4 ; 2 (a) Find all the Nash equilibria, pure and mixed. Explain how you know you have found all the equilibria. (b) Suppose that the payo& of the column player u 2 ( D;l ) is reduced from 8 to 6, but all other payo&s remain the same. Again, nd all the pure and mixedstrategy Nash equilibria. (c) Compare the mixedstrategy equilibria in parts (a) and (b). Did this worsening in one of player 2s payo&s change player 2s equilibrium mixed strategy? Did it change player 1s? Give some intuition. 2. On Her Majestys Secret Service. The famous British spy 001 has to choose one of four routes a , b , c , or d (listed in order of speed in good conditions) to ski down a mountain. Fast routes are more succeptible to avalanche. At the same time, the notorious rival spy 002 has to choose whether to use (\ y ") or not to use (\ x ") his valuable explosive to try to cause an avalanche. The payo&s to this game are as follows....
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This note was uploaded on 02/13/2012 for the course ECON 159 taught by Professor Benjaminpolak during the Fall '08 term at Yale.
 Fall '08
 BENJAMINPOLAK
 Game Theory

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