This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 » (3 , 2) (1 , 1) (1 , 1) (2 , 3) – , show that a purestrategy Nash equilibrium profile is for the players both to play C on oddnumbered stages and B on evennumbered stages. 2. We say that a pure action ˆ a i for Player i in an nperson game is strictly dominant if and only if u i ( a 1 , . . . , ˆ 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 ˜ a i for Player i in an nperson game is strictly dominated if and only if u i ( a 1 , . . . , ˜ 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 “Play D” is strictly dominant for each player in the Prisoner’s Dilemma with the payoffs in the book. (b) Show that in any game, a purestrategy Nash equilibrium profile will never feature a strictly dominated strategy....
View
Full Document
 Spring '07
 DELCHAMPS
 Algorithms, Game Theory, purestrategy Nash equilibrium, replicator dynamics, best reply, Nash equilibrium profile

Click to edit the document details