Problem 5 (15 points). The simultaneous move game below is played twice, with the outcome of the first stage observed before the second stage begins. L C R T 3,1 0,0 5,0 M 2,1 1,2 3,1 B 1,2 0,1 4,4 Assume there is no discounting. Can the payoff (4, 4) be achieved in the first stage in a pure strategy subgame perfect equilibrium? If so, give strategies that do so. If not, prove why not. Problem 6 (15 points). Consider the following stage game. C D C 6,6 0,8 D 0,2 4,0 (a) (3 points) Find all pure and mixed strategy Nash equilibria of the stage game. Calculate the expected payoffs in equilibrium. (b) (3 points) Suppose that the stage game is repeated 91 times. Find all subgame perfect Nash equilibria of the repeated game. (c) (9 points) Suppose that the stage game is repeated infinitely many times and the discount factor is 8 [0,1]. Is there a subgame perfect Nash equilibrium in pure strategies in which (C,C) is played in every round?