1. Consider a two-period game between two players. The players play the prisoners' dilemma in the first period with the payoffs given below Player 2 C D Player 1 C 3, 3 0, 4 D 4, 0 1, 1 The payoffs in the second period are given below: Player 2 C D Player 1 C 3, 3 0, 0 D 0, 0 1, 1 The total payoff is the sum of the payoffs from each period. (a) Give the set of pure strategies for each player. (b) Does there exist a subgame perfect equilibrium in which each player chooses C in the first period? If yes, find one such equilibrium. If not, explain why not. (c) Does there exist a Nash equilibrium that is not a subgame perfect equilibrium? If yes, find one such Nash equilibrium. If not, explain why not