Consider an infinitely repeated game in which 2 identical firms simultaneously choose prices in each period. The firms sell a homogeneous product, and face a production technology with total costs equal to zero. Assume that the industry demand curve is given by Q=100-P. Each firm discounts future profits with the same discount factor0<<1.

Suppose that the firms attempt to enforce collusion at the monopoly price with the threat of reverting to the static Nash equilibrium price if anyone deviates. Suppose further that the firms use symmetric strategies.

(a) Specify precisely each firm's strategy.

(b) Derive the condition that must be satisfied for no firm to have an incentive to cheat on the collusive agreement.

(c) Suppose now that the game is repeated for two periods only. Is collusion sustainable in equilibrium? Why or why not?