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04solution

# 04solution - Prof William H Sandholm Department of...

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–1– Prof. William H. Sandholm Department of Economics University of Wisconsin March 11, 2004 Midterm Exam Solutions – Economics 713 1. (i) G and G need not have the same perfect equilibria. For example, removing one of player 1’s strategies can cause one of player 2’s strategies to become weakly dominated, so that it can no longer be a part of a perfect equilibrium. (ii) G and G must have the same value: the games have the same set of Nash equilibria, and the value of any zero sum game is the payoff achieved by player 1 in all of its Nash equilibria. (This payoff is unique by the Minmax Theorem.) 2. (i) The two extreme cases occur when Johnny likes p and r equally and less than q , and when Johnny likes q and r equally and strictly less than p . It is easily verified by drawing a picture of the possible indifference curves that if Johnny likes r at least as much as s in these two cases, then he likes r at least as much as s under any preferences satisfying the constraints stated in the question. Now an NM utility function for the first extreme case is ( u a , u b , u c

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04solution - Prof William H Sandholm Department of...

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