Problem 3 Consider the infinitely repeated game with the discount factor 8 € (0, 1) of the following Cournot duopoly model with inverse demand function P(Q) :{ = a- 0 where Q = 91 +92 and cost functions Ci(qi) given by = Q if Q ≤ a if Q > a cqi, i 1,2. The profit function of firm i is Ti (91, 92) = qiP(q₁ +92) - cqi. Consider the following grim-trigger strategy. Produce half the monopoly output in the first period and as long as everybody has produced that amount so far. Otherwise produce the Cournot output. Verify that this is a subgame perfect equilibrium.
Problem 3 Consider the infinitely repeated game with the discount factor 8 € (0, 1) of the following Cournot duopoly model with inverse demand function P(Q) :{ = a- 0 where Q = 91 +92 and cost functions Ci(qi) given by = Q if Q ≤ a if Q > a cqi, i 1,2. The profit function of firm i is Ti (91, 92) = qiP(q₁ +92) - cqi. Consider the following grim-trigger strategy. Produce half the monopoly output in the first period and as long as everybody has produced that amount so far. Otherwise produce the Cournot output. Verify that this is a subgame perfect equilibrium.
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.4P
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