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PS2_212Fal10

# PS2_212Fal10 - ECON 212 Game Theory Fall 2010 Prof Andrew...

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ECON 212 Game Theory Prof. Andrew Postlewaite Fall 2010 University of Pennsylvania Suggested Solution for Problem Set 2 1. Osborne 48.1 Let 2 n +1 be the number of citizens. The Nash equilibria of the game are as follows. (i) n + 1 citizens vote for A and all of them prefer A to win. Consider a citizen who votes for A according to this action pro°le. If he deviates (votes for B), then B is chosen, which is a worse outcome for him, so he doesn±t deviate. Given that n + 1 votes for A, no one who votes for B can±t change the outcome by unilaterally deviating, so no one has an incentive to deviate. (ii) More than n + 3 citizens vote for either A or B. No citizen can change the outcome by unilateral deviation. The action pro°le that everyone votes for his or her own candidate is an equilibrium in which no player uses a weakly dominated action. 2. Osborne 49.1 Suppose a citizen prefers A to B, and B to C. (1) Voting for either A or B is not weakly dominated.

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