9. (a) Consider the following extensive-form game with two players, 1 and 2. Out (4,3) In B C D C D (3,1) (5,0) (2,4) (6,6) i. Find the pure-strategy Nash equilibria of the subgame that starts after player 1 plays "In." (Hint: Write down the normal form of the subgame and find the pure-strategy Nash equilibria.) [5 marks] ii. Find the pure-strategy subgame-perfect equilibria of the game. (Hint: For each Nash equilibrium of the subgame, find the optimal action of 1 at the initial node to find the subgame-perfect Nash equilibria.) [5 marks] (b) Suppose the following game is repeated infinitely. The players have a com- mon discount factor & e (0, 1). 2 C D 1 C 3,3 0,5 5,0 1,1 i. Find the value &* such that cooperation (ie. playing (C, C) every pe- riod) can be sustained as an equilibrium of the infinitely repeated game for 6 3 6*. [5 marks] ii. For what values of & is it possible to sustain playing (D, D) each period as an equilibrium of the infinitely repeated game? [5 marks]