13. (a) Find the pure and mixed strategy Nash equilibria of the following game. [8 marks] Player 2 Player 1 A| 2,7 3,2 B1 0.0 (b) Consider the following extensive-form game with two players, Player 2 moves after player 1. Each player can produce a high output or a low output. Player 1's payoff is additionally influenced by an exogenous event which occurs with probability pe [0, 1]. The payoffs are written as ((Payoff to 1), Payoff to 2). LI HI ((4 -2p),1) ((3-2p).4) ((2 + p).2) ((1+ p).1) I Suppose p > 1/3. Find the subgame perfect Nash equilibrium of the game above. [6 marks] ii. Suppose, before the start of the game, player 2 has the option of com- mitting to produce a high output (H2). Making such a commitment requires player 2 to incur a cost of 1. Find the range of values of p for which it is optimal to make such a costly commitment. [6 marks]