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Problem_Set_9_solutions

Problem_Set_9_solutions - ECON W3211.002 Intermediate...

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ECON W3211.002 Intermediate Microeconomics Problem Set 9 Due Monday December 6, 2010 Solutions 1. Perloff, Chapter 14, Problem 23 Here we need to make an assumption to make the problem amenable to our Nash equilibrium analysis. The assumption is that if only one swimmer takes steroids, then that swimmer wins. If both players make the same decision regarding steroids, then the race results in a tie. The payoff matrix is therefore Swimmer 2 Take Don’t take Take 4, 4 14, 0 Swimmer 1 Don’t take 0, 14 10, 10 a. The Nash equilibrium is is for both swimmers to take steroids. The game is a prisoners’ dilemma because both swimmers would prefer to cooperate to abstain from steroids. b. Suppose Swimmer 1’s utility of taking steroids is now -12. Now the payoff matrix is Swimmer 2 Take Don’t take Take -2, 4 8, 0 Swimmer 1 Don’t take 0, 14 10, 10 The Nash equilibrium is where Swimmer 1 abstains and Swimmer 2 takes steroids. The game is no longer a prisoners’ dilemma because there is no outcome that is preferrable for both swimmers.
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