04exam - Prof. William H. Sandholm Department of Economics...

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–1– Prof. William H. Sandholm Department of Economics University of Wisconsin March 11, 2004 Midterm Exam – Economics 713 1. (15 points) Let G be a two player normal form game, and let G be another normal form game obtained from G by removing a strictly dominated strategy. (i) Must G and G have the same perfect equilibria? Prove that they must, or provide an example showing that they need not. (ii) Suppose in addition that G is zero-sum. Must G and G have the same value? Prove that they must, or construct an example showing that they need not. 2. (20 points) Johnny’s preferences concerning lotteries over artichokes, bell peppers, and carrots satisfy the von Neumann-Morgenstern axioms. Define three lotteries over these vegetables as follows: p = ( p A , p B , p C ) = ( 1 2 , 1 2 , 0), q = (0, 2 3 , 1 3 ), and r = ( 1 3 , 1 3 , 1 3 ). Suppose we know that Johnny likes both p and q at least as much as he likes r , and that he likes at least one of these strictly more than he likes r , but that we don’t know Johnny’s preferences between p
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This note was uploaded on 08/08/2008 for the course ECON 713 taught by Professor Sandholm during the Spring '08 term at Wisconsin.

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04exam - Prof. William H. Sandholm Department of Economics...

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