On Globally Optimal Punishments in the Repeated Cournot Game

We challenge the global optimality of one-shot punishments in infinitely repeated games with discounting. Specifically, we show that the stick-and-carrot punishment à la Abreu (1986) may not be globally optimal. We prove our result by investigating tacit collusion in the infinite repetition of a linear Cournot game. We illustrate the existence of the stick-and-carrot globally optimal punishment for large cartels, and fully characterise it. Then, we show that for mall cartels, global optimality may be reached only with two-period punishments.