# 03exam - Prof William H Sandholm Department of Economics...

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–1– Prof. William H. Sandholm Department of Economics University of Wisconsin March 13, 2003 Midterm Exam – Economics 713 1. (10 points) Let G be a two player zero sum game. Show that if σ 1 S 1 is a strategy of player 1 which minmaxes player 2, then σ 1 is not strictly dominated. 2. (10 points) You and a friend are computing the subgame perfect equilibria of an infinitely repeated game G ( ) δ . Your friend suggests that to perform the computation efficiently, you should begin by eliminating all dominated actions from the stage game. Evaluate your friend’s suggestion. 3. (15 points (5, 10)) A (finite) normal form game G is a potential game if there exists a function P : S R (known as a potential function ) such that u i ( s i , s i ) – u i ( s i , s i ) = P ( s i , s i ) – P ( s i , s i ) for all s i , s i S i , s i S i , and i N . ( i ) Explain in words what this condition means. ( ii ) Prove that every potential game has at least one pure strategy Nash equilibrium.

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