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# 07exam - Prof William H Sandholm Department of Economics...

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Prof. William H. Sandholm Department of Economics University of Wisconsin March 13, 2007 Midterm Exam – Economics 713 1. (15 points) Suppose that two players repeatedly play the following normal form game: 2 T M B T 3, 3 2, 1 - 2 , 4 1 M 1, 2 1, 1 - 1 , 3 B 4 , - 2 3 , - 1 0, 0 Suppose that strategy σ i for player i is described as follows: Begin play in stage I. (I) If T has always been played, play T . Otherwise, begin stage II. (II) If M has always been played since stage II began, play M ; otherwise, begin stage III. (III) Play B . For what values of δ is strategy profile σ = ( σ 1 , σ 2 ) a subgame perfect equilibrium? 2. (15 points) Let G = { N , { A i } i N , { u i } i N } be a normal form game. Let Γ = { N , { T i } i N , p , { A i } i N , { u i } i N } be a Bayesian game with common prior distribution p Δ T , and with the same action sets A i and utility functions u i : A R as G . Note that u i does not condition on players’ types. (i) Describe S i , the set of of player i ’s pure strategies in Γ .

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