Suppose there are two firms that compete on prices. Thus, each firm chooses a price and then produces enough quantity to meet the demand it faces, given the prices chosen by both firms. Assume that if the prices chosen by the firms are different, then all consumers purchase the good from the firm with the lower price. The firm with the higher price receives no demand and produces no output. If both firms set the same price, they

split the demand equally at that common price. Suppose the marginal cost of production for both firms is identical and constant, i.e. c. Further, the demand at price p is D(p) and profits, given by (p) = (p c)D(p), are maximised at the monopoly price p_m. Now, let the strategy of firm i where i = 1, 2 in the infinitely repeated game be:

-charge p_m in the first period.

-charge p_m subsequently as long as the other firm continues to charge p_m and punish any deviation from p_m by the other firm by choosing c for k periods, and then reverting to p_m.

Given any value of , where (0, 1) is the discount factor, for what value of k is this strategy a Nash equilibrium of the infinitely repeated game? [15]