game theory

Consider a collusion game. Suppose there are two identical firms with costs c(q) = 10q facing demand P = 200 2Q.

(a) Find the payoffs of the collusion matrix game, i.e., find profits when both firms collude to behave like a monopoly, when they both operate like oligopoly and when one of them colludes and the other does not. (Round the profits for simplicity.)

(b) Find discount factor , for which the collusion is sustainable.