Extremal equilibria of oligopolistic supergames

General propositions established in Abreu (Ph.D. thesis, Princeton University, October 1983) are applied to the analysis of optimal punishments and constrained Pareto optimal paths of symmetric oligopolistic supergames. A remarkably simple 2-dimensional stick-and-carrot characterization of optimal symmetric punishments is obtained. An analogous result holds for the general case of asymmetric punishments, motivating the study of asymmetric Pareto optimal paths. The latter turn out to have a highly non-stationary dynamic structure which sometimes entails intertemporal reversals of relative payoffs between firms.