Anomalies in strongly symmetric equilibria of repeated Cournot oligopolies

Abstract We examine strongly symmetric equilibrium (SSE) payoff sets in a general repeated Cournot oligopoly. In a seminal paper, Abreu (1986) shows that the entire set of SSE payoffs can be constructed through simple two-phase (“stick-and-carrot”) punishment paths. However, we find that for many commonly used demand functions, the resulting SSE payoff set can be non-convex, and the quantities and payoffs associated with the best and worst SSEs can exhibit discontinuities in the discount factor. To resolve these issues, we propose regularity conditions that prevent such anomalies in SSE payoffs. Beyond our baseline model, we demonstrate that similar anomalies also arise in other important applications of Abreu’s optimal symmetric punishments in the literature. Our findings highlight the need for caution when applying stick-and-carrot punishments in collusion analysis across different scenarios.