06exam - Prof. William H. Sandholm Department of Economics...

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Prof. William H. Sandholm Department of Economics University of Wisconsin March 9, 2006 Midterm Exam – Economics 713 1. (20 points) Let G be a two player normal form game, and suppose that players are only allowed to choose pure strategies. Only one of the following statements must be true: (A) min s 2 ± S 2 max s 1 ± S 1 u 1 ( s 1 , s 2 ) ± max s 1 ± S 1 min s 2 ± S 2 u 1 ( s 1 , s 2 ) ; (B) min s 2 ± S 2 max s 1 ± S 1 u 1 ( s 1 , s 2 ) ² max s 1 ± S 1 min s 2 ± S 2 u 1 ( s 1 , s 2 ) . Prove the statement that must be true, and provide an example in which the other statement is false. 2. (35 points) Compute all perfect Bayesian equilibria and sequential equilibria of the game below.
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3. (15 points) Let ± be a perfect information extensive form game, and let G ( ) be its reduced normal form. (i) Must every perfect equilibrium of G ( ) correspond to an extensive form perfect equilibrium of ? Prove that this is true, or provide a counterexample. (ii)
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06exam - Prof. William H. Sandholm Department of Economics...

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