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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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