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Consider a Cournot duopoly with two firms, i = 1,2. Each company has a cost of production c(qi) = 10qi. The market demand function is P = 130-Q, Q = q1 +q2. Consider an infinitely repeated version of this game, where in each period each company decides to collude or not to collude. When it chooses collusion, a company produces half of the monopoly level of output. When it chooses no collusion, a company produces the Cournot level of output. Prove that, for some value of the discount factor δ, there is a profile of strategies that is a subgame perfect equilibrium.
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