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problemset4

# problemset4 - Problem Set 4 Ben Polak Econ 159a/MGT522a...

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Problem Set 4. Ben Polak Econ 159a/MGT522a Three questions due October 10, 2007 (1) Comparative Statics of Mixed Strategy Equilibria. Consider the following two-player 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 mixed-strategy Nash equilibria. (c) Compare the mixed-strategy equilibria in parts (a) and (b). Did this worsening in one of player 2’s payo°s change player 2’s equilibrium mixed strategy? Did it change player 1’s? Give some intuition. 2. On Her Majesty’s 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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problemset4 - Problem Set 4 Ben Polak Econ 159a/MGT522a...

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