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Unformatted text preview: ECON 212 Game Theory (Honors) Fall 20 10 U ni versity o f P e n nsylva n ia Suggested Solution for Problem Set #1 1. Gibbons 1.3 Description of the game: I = { 1 , 2 } , S 1 = S 2 = [0 , 1] , and u i ( s i , s j ) = s i if s i + s j 1 otherwise Consider player 2s problem. Given player 1s strategy a 1 , player 2s best response is r 2 ( a 1 ) = 1 a 1 if a 1 < 1 [0 , 1] if a 1 = 1 We can f nd player 1s best response similarly. Using the fact that r 2 ( a 1 ) = a 2 and r 1 ( a 2 ) = a 1 in equilibrium, we conclude that the set of purestrategy Nash equilibria is { ( t, 1 t ) : t [0 , 1] } { (1 , 1) } . 2. Gibbons 1.4. The equilibrium is ( q 1 , ..., q n ) with which no f rm can increase pro f t by changing quantity unilat erally. Consider player 1s problem. Given ( q 2 , ..., q n ) , his problem is max q 1 ( P ( q 1 + ... + q n ) c ) q 1 Assuming P ( q 1 + ... + q n ) > c , his optimal solution q 1 satis f es ( a ( q 1 + .......
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This note was uploaded on 02/29/2012 for the course GG 101 taught by Professor Gg during the Spring '12 term at UPenn.
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