The Cournot–Theocharis problem reconsidered

In 1959 Theocharis [Theocharis RD. On the stability of the Cournot solution on the oligopoly problem. Review of economic Studies 1959;27:133–4] showed that with linear demand and constant marginal costs Cournot equilibrium is destabilized when the competitors become more than three. With three competitors the Cournot equilibrium point becomes neutrally stable, so, even then, any perturbation throws the system into an endless oscillation. Theocharis’s argument was in fact proposed already in 1939 by Palander [Palander T. Konkurrens och marknadsjämvikt vid duopol och oligopol. Ekonomisk Tidskrift 1939;41:124–45, 222–50]. None of these authors considered the global dynamics of the system, which necessarily becomes nonlinear when consideration is taken of the facts that prices, supply quantities, and profits of active firms cannot be negative. In the present paper, we address the global dynamics.