9. (a) Consider the following simultaneous move game with two players. 2 1 3.1 1,2 B1 1.2 3,1 Consider the pure strategies of player 1. Note that A, does not dominate By, and By does not dominate Aj. Is it possible for a mixed strategy of player 1 to be a dominant strategy? Explain. [5 marks] (Hint: For any mixed strategy of 1 to be a dominant strategy, it must dom- inate both A, and Bj. Is this possible?) (b) For the following extensive-form game: i. Identify the pure and mixed strategy Nash Equilibria. [5 marks] ii. Identify all Subgame Perfect Nash equilibria. [5 marks] A 2 C D D (3,2) (1,-1) (-1,0) (2,3) (c) Suppose the following game is repeated infinitely. The players have a com- mon discount factor & E (0, 1). Show that for high enough values of $, there is an equilibrium of the infinitely repeated game in which (C, C) is played in every period. Your answer must state the strategies of the players clearly. [5 marks] 2 C D 1 C 4,2 D 5.0