## 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: