Game theory

Two players play the following stage-game twice in a row (T = 2), and observe each other's first-stage action before choosing actions in the second stage. Both players discount second-stage payoffs using a discount factor o e [0, 1]. (a) [2 points] Find all pure-strategy Nash equilibria of the stage game. 2 L C R T 3, 2 0,0 15,0 M 2, 1 1, 2 3, 1 B 1, 2 |0, 1 4,4 (b) [1 point] How many pure strategies does each player have in the two-stage game? (c) [4 points] What is the smallest o for which the profile (B, R) can be played in the first stage of a pure-strategy subgame perfect equilibrium for the two-stage game? (d) [3 points] Can the strategy profile (T, R) be played in the first stage of a pure-strategy subgame perfect equilibrium for 6 = 1? If yes, describe the equilibrium strategies. If not, explain why not