Exercise 1. Suppose that player 1 and player 2 participate in an infinitely repeated game, where each stage of the game is the Prisoner's Dilemma game shown below. As described in the lectures and textbook, the payoff for each player is a discounted sum of the payoffs for each stage, with discount factor 0 < < 1: if pn denotes a player's payoff in stage n, then that player's payoff for the repeated game is n=0 n pn = p0 p1 2 p2 Player 2 C D Player 1 C 5, 5 8, 8 D 8, 8 0, 0 (a) Let denote the trigger strategy. Suppose that player 1 plays in the repeated game. Explain in words what this means. (b) Let denote the tit-for-tat strategy: Begin by playing C. Thereafter, play whatever the other player played in the previous round. Find the payoffs when player 1 plays and player 2 plays : 1( , ) and 2( , ) It should be clear in your work which move each player plays in each stage (you can explain this, or you can demonstrate an established pattern as