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In a duopoly with an infinite life span, firms may agree to jointly produce, as a monopoly, or compete in the Cournot fashion. In the

In a duopoly with an infinite life span, firms may agree to jointly produce, as a monopoly, or compete in the Cournot fashion. In the first case, in each period, each would have a profit of 100 and, in the second, of 50. However, if one of the firms betrays the agreement and acts opportunistically in a certain period, while the other company maintains the agreed amount, its profit would be 200 in that period, while in the following ones the agreement would be undone, and the firms started to compete in the Cournot style. There is a financial asset that offers fixed income of 100.(r)% per period. What is the value of "r" that leaves firms indifferent between acting as a monopoly or betraying the coalition?

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