Problem 3Consider the infinitely repeated game with the discount factor & € (0, 1) of the followingCournot duopoly model with inverse demand functionP(Q) =a Q if Q≤ a0if Q > awhere Q = 91 +92 and cost functions Ci(qi) = cqi, i = 1,2. The profit function of firm i isgiven byTi (91, 92) = qiP(9₁ +92) - cqi.Consider the following grim-trigger strategy. Produce half the monopoly output in the firstperiod and as long as everybody has produced that amount so far. Otherwise produce theCournot output. Verify that this is a subgame perfect equilibrium.

In game theory, a grim trigger strategy is a type of cooperative strategy used in repeated games,…

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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.4P

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