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# ps3 - 14.12 Game Theory Muhamet Yildiz Fall 2005 Homework 3...

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14.12 Game Theory Muhamet Yildiz Fall 2005 Homework 3 Due on 10/31/2005 1. Two players fi rst simultaneously declare Yes or No. If any of the player declares No, then each player gets 80. If both players declare Yes, then they play the following game: Invest Consume Invest 100, 100 0, 60 Consume 60, 0 60, 60 Find all the subgame-perfect equilibria of the entire game. 2. Consider the bargaining game discussed in the class, where two players try to divide a dollar, which they cannot consume until they divide, and the payo ff from getting share x at t is δ t 1 x . At each date a player proposes a division ( x, 1 x ) , and the other player accepts or rejects. If the o ff er is accepted, then it is implemented, ending the game; otherwise, we proceed to the next date. The order of proposers is Player 1, Player 1, Player 2, Player 1, Player 1, Player 2, Player 1, . . . , i.e., Player 1 makes two o ff ers for each o ff er of Player 2. (a) Assume that the game ends at date 3 n , after which players get 0. Use backwards induction to compute an equilibrium.

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ps3 - 14.12 Game Theory Muhamet Yildiz Fall 2005 Homework 3...

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