10. (a) Consider the following simultaneous-move game with two players, 1 and 2. Show that each player playing each pure strategy with equal probability is a mixed-strategy Nash equilibrium of the game. [6 marks] Player 2 M H 574 3,4 15 Player 1 M 4,3 0.2 H (b) Consider the following extensive-form game with two players, Initially, Player 1 can either play Pi to keep the game going, or play S, to end the game. If Player 1 chooses A, Player 2 then chooses between P, and $2. Finally, if 2 chooses Pr, Player 1 can choose between Py and $3. The payoffs are written as (Payoff to 1, Payoff to 2). Identify any subgame perfect Nash equilibrium. [6 marks] 2.0 1.2 33 (c) Two firms face the following strategic pricing problem. Each firm can set a high price H or a low price L. The payoffs are as follows: Firm 2 H Firm 1 L 5,- -1,5 2.2 Suppose this pricing game between the firms is repeated infinitely. Firms discount the future, so that, for each firm, a payoff of x received / periods from today is worth &x today, where 0