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The Cournot-Theocharis problem reconsidered. (English) Zbl 1140.91444
Summary: In 1959, R. D. Theocharis [On the stability of the Cournot solution on the oligopoly problem. Rev. Econ. Stud. 27, 133–134 (1959)] 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 T. Palander [Konkurrens och marknadsjämvikt vid duopol och oligopol. Ekonomisk Tidskrift 41, 124–45, 222–250 (1939)]. 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.

MSC:
91B52 Special types of economic equilibria
37N40 Dynamical systems in optimization and economics
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