zbMATH — the first resource for mathematics

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.

91B52 Special types of economic equilibria
37N40 Dynamical systems in optimization and economics
Full Text: DOI
[1] Cournot, A., Recherches sur LES principes mathématiques de la théorie des richesses, (1838), Hachette Paris · Zbl 0174.51801
[2] Edgeworth, F.Y., La teoria pura del monopolio, Giorn econ, 15, 13-31, (1897)
[3] Palander T. Instability in competition between two sellers, in: Abstracts of Papers Presented at the Research Conference on Economics and Statistics held by the Cowles Commission at Colorado College, Colorado College Publications, General Series No. 208, Studies Series No. 21, 1936.
[4] Palander, T., Konkurrens och marknadsjämvikt vid duopol och oligopol, Ekon tidskr, 41, 124-145, (1939), 222-250
[5] Puu, T.; Suskho, I., Oligopoly dynamics – models and tools, (2002), Springer-Verlag
[6] Puu T. On the stability of Cournot equilibrium when the number of competitors increases, submitted for publication.
[7] Okuguchi, K., Expectations and stability in oligopoly models, (1976), Springer-Verlag · Zbl 0339.90010
[8] Robinson, J., The economics of imperfect competition, (1933), Macmillan London
[9] Tuinstra, J., Oligopoly dynamics: models and tools, J econ behav org, 54, 611-614, (2004)
[10] Theocharis, R.D., On the stability of the Cournot solution on the oligopoly problem, Rev econ stud, 27, 133-134, (1959)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.