Question on Game Theory

4. (25 points) Consider the following one-shot simultaneous-move game: L C R U (a;0) (0;4) (0;5 M (2;0) (1;1) (0;0) D (0;0) (0;0) (3;3) a) Give all Nash equilibria in pure strategies. For parts b and c below, the game is played twice, with both players observing the outcome of the first periods play before playing the second period with common discount factor 8 = 1. For both parts, consider only pure strategies. b) Give a subgame-perfect Nash equilibrium in which (U, C) is played in the first period. c) For what values of a does there exist a SPNE in which (M, L) is played in the first period? Give the SPNE. For part d, the game is repeated infinitely often with common discount factor S. d) Find the minimum value of the common discount factor, o, such that the players can reach an average discounted payoff of 3 in a SPNE of the infinitely repeated game? Give the strategies and show your work