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 f 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 f from getting share x at t is δ t 1 x . At each date a player proposes a division ( x, 1 x ) ,andthe other player accepts or rejects. If the o f 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 f ers for each o f er of Player 2. (a) Assume that the game ends at date
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ps3 - 14.12 Game Theory Muhamet Yildiz Fall 2005 Homework 3...

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