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(25 pts) Consider the game consisting of the prisoner's dilemma below repeated infinitely many times Assume both players have the discount factor 8 0.5.2,2 8,...

Question

(25 pts) Consider the game consisting of the prisoner's dilemma below repeated infinitely many times Assume both players have the discount factor 8 0.5.2,2 8,0 N 0,8 4,4 (5 pts) Compute player 1's payoff when each player has the strategy "Confess after every history" Show your work: b (10 pts) Show that the strategy profile in which each player plays "Confess after every history" is subgame perfect equilibrium. Show all your work: It will help to use the one-deviat

(25 pts) Consider the game consisting of the prisoner's dilemma below repeated infinitely many times Assume both players have the discount factor 8 0.5. 2,2 8,0 N 0,8 4,4 (5 pts) Compute player 1's payoff when each player has the strategy "Confess after every history" Show your work: b (10 pts) Show that the strategy profile in which each player plays "Confess after every history" is subgame perfect equilibrium. Show all your work: It will help to use the one-deviation property: (10 pts) The tit-for-tat strategy is (Not Confess in period 1; Confess in period n if the opponent has confessed in period n 1; Not Confess in period n if the opponent has not confessed in period n 1). Determine whether the strategy profile in which each player plays the tit-for-tat strategy is subgame perfect equilibrium It will help to use the one-deviation property:



Answers

Consider a game with two players who cannot communicate, and in which each player is asked a question. The players can answer honestly or lie. If both answer honestly, each receives $\$ 100$. If one player answers honestly and the other lies, the liar receives $\$ 500$ and the honest player gets nothing. If both lie, then each receives $\$ 50$. a. Describe the strategies and the payoffs. b. Construct the payoff matrix. c. What is the equilibrium of this game? d. Compare this game to the prisoners' dilemma. Are the games similar or different? Explain.


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