4. Two firms A and B can choose to Cooperate (C) or Defect (D). The payoff to each firm is given in the table below: B C D A 4,5 0,9 D 9,0 a, b (a) Give a necessary and sufficient condition on a and b for the strategy profile (D,D) to be a Nash equilibrium. (3) Assume that a = 2 and b = 1. (b) Calculate all the pure and mixed strategy Nash equilibria of this game. (6) (c) Suppose that A moves first and announces its intention as regarding cooperating with B. Calculate the subgame perfect equilibria. (3) (d) Assume that the game is repeated infinitely. The discount rate is r. The players adopt the punishment strategy of defecting in the current period if either player defected in the last period. How large can r be for cooperation to be sustained as a Nash equilibrium? (7)