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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 Spring '12
 gg
 Game Theory, mixed strategy equilibrium, action pro…le

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