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3. Consider the following simultaneousmove game. For this problem, we shall restrict our attention to pure strategies only. Player 1 has three actions: A, B? and 0; player 2 has three actions: L? M, and R_| L M R (a) (5 points) Find all pure strategy Nash equilibria of this game. (b) (5 points) Suppose N = 2. Elhowr that [B] L) and then (CTR) can be played on the equilibrium path of some pure strategy subgame perfect equilibrium. Please specify the strategy of each player and explain why the strategy prole forms a subgame perfect equilibrium (c) (10 points) Suppose N = 3. Can (B, M), (B, M), and (A, L), in that order, be played in some pure strategy subgame perfect equilibrium? Explain your answer. (d) (10 points) Now consider the infinitely repeated play of the stage game above. Assume the two players discount their payoffs using a common discount factor o e (0, 1) . Is there a pure strategy subgame perfect equilibrium in which player I's average payoff is 0.5 when the discount factor o is sufficiently close to 1? Explain