Problem 2 (Required, 35 marks) We consider an infinite repeated games which a static games G is played repeatedly. The payoff matrix of the games G is given by Player 2 a b c Player 1 a (6,6) (2,9) (0,30) b (9,2) (3,3) (0,0) c (30,0) (0,0) (1,1) We let D (0,1] be the discounting factor (a) Show that when D is sufficiently large, there exists a subgame perfect equilibrium which two players plays (a, a) in every round of the games. What are the average payoff of two players? (b) Show that when D is sufficiently large, there exists a subgame perfect equilibrium (with public randomization) which both players can receive an average payoff higher than that in (a). What is the corresponding strategic profiles? (c) Using one-stage deviation principle, show that when D is sufficiently large, there exists a subgame perfect equilibrium (without public randomization) which both players can receive an average payoff higher than that in (a). What is the corresponding strategic profiles