1. Let market demand be given by Q = 200 - P. Each firm's cost function is C(qi) = 20qi, where i = 1, 2.
(a) Using the Cournot model, find each firm's output, price and profit.
(b) Suppose that the duopolists collude. Find their joint profit-maximizing price, output, and profit.
(c) Suppose now that each firm has two strategies: Cooperate or Defect. If a firm plays Cooperate, it chooses half of the collusive quantity level in (b).
If a firm plays Defect, it chooses the noncooperative quantity level in (a). Present the 2-by-2 matrix game, determine the Nash equilibrium outcome, and discuss the implications of the outcome.
(d) Suppose the game in (c) is repeated infinitely many times. Each firm has a discount factor δ. Determine the critical discount factor above which cooperation between the two firms can be sustained (i.e., playing grim trigger strategy by both firms is an equilibrium in the repeated game).