Question: Cournot duopolists face the inverse demand function p = 200 - 0.5X, where p is selling price and X is the total output of both firms. Long-run marginal costs are a constant 50 for both firms.
(a) Along the lines suggested in Box 17.1 construct the payoff matrix if the two firms ‘stick to a cartel' and ‘cheat on a cartel'. Confirm that the payoffs involved define a prisoners' dilemma game.
(b) If both firms adopt a tit-for-tat strategy, what is the maximum discount rate that is consistent with cartel stability?