Beyond myopic best response (in Cournot competition)

The Nash equilibrium as a prediction myopically ignores the possibility that deviating from the equilibrium could lead to an avalanche of beneficial changes by other agents. We consider a non-myopic version of Cournot competition, where each firm selects either profit maximization (as in the classical model) or revenue maximization (by masquerading as a firm with zero production costs). We consider many non-identical firms with linear demand functions and show existence of pure Nash equilibria, that simple dynamics will produce such an equilibrium, and that some natural dynamics converge within linear time. Furthermore, we compare the outcome of the non-myopic Cournot competition with that of the standard Cournot competition. Prices in the non-myopic game are lower and the firms, in total, produce more and have a lower aggregate utility. We also briefly consider a non-myopic version of Bertrand competition, and find that prices increase relative to the classical model.