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Unformatted text preview: ECE 496 HOMEWORK ASSIGNMENT V Spring 2007 1. In the finitely repeated (with summed payoffs) Battle of the Sexes/Brothers C B C B Â» (3 , 2) (1 , 1) (1 , 1) (2 , 3) â€“ , show that a pure-strategy Nash equilibrium profile is for the players both to play C on odd-numbered stages and B on even-numbered stages. 2. We say that a pure action Ë† a i for Player i in an n-person game is strictly dominant if and only if u i ( a 1 , . . . , Ë† a i , . . . , a n ) > u i ( a 1 , . . . , a i , . . . , a n ) for all other actions a i for player i and all choices of actions a j , j 6 = i , for the opposing players. On the other hand, we say that an action Ëś a i for Player i in an n-person game is strictly dominated if and only if u i ( a 1 , . . . , Ëś a i , . . . , a n ) < u i ( a 1 , . . . , a i , . . . , a n ) for some other action a i for player i and all choices of actions a j , j 6 = i , for the opposing players. (a) Show that the strategy â€śPlay Dâ€ť is strictly dominant for each player in the Prisonerâ€™s Dilemma with the payoffs in the book. (b) Show that in any game, a pure-strategy Nash equilibrium profile will never feature a strictly dominated strategy....
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This note was uploaded on 02/01/2010 for the course ECE 496 taught by Professor Delchamps during the Spring '07 term at Cornell.
- Spring '07