On the stability of Cournot equilibrium when the number of competitors increases

Abstract

This article reconsiders whether the Cournot equilibrium really becomes a perfect competition equilibrium when the number of competitors goes to infinity. It has been questioned whether the equilibrium remains stable with an increasing number of firms. Contraindications were given for linear and for isoelastic demand functions. However, marginal costs were then taken as constant, which means adding more potentially infinite-sized firms. As we want to compare cases with few large firms to cases with many small firms, the model is tuned so as to incorporate capacity limits, decreasing with an increasing number of firms. Then destabilization is avoided

On the existence of ɛ-fixed points

“…Assume F : X → P c (X ) is a map satisfying the following properties: We hope that the results presented in this paper can help the study of all games having an intractability proving the existence of a Nash equilibrium (see for example [2,8], etc.) and support the research on Cournot-Nash equilibrium in the dynamic nonlinear oligopoly theory, recently studied by Puu in [10].…”

The Cournot–Theocharis problem reconsidered

“…An increasing number of firms should then decrease the capacity limits for the individual firms. A way to do this, through splitting a given total capacity of an industry between more or less numerous firms, was proposed in [6].…”

“…Now, this picture presupposes that we use an increasing marginal cost curve, otherwise the marginal cost curve and the demand curve never intersect. Such a marginal cost curve (which also incorporated an asymptotic capacity limit) was suggested in [6], but there are many alternatives. Anyhow, the destabilization of the Cournot point does not have any great importance in the basic issue of the relation between Cournot oligopoly and perfect competition.…”

Price-Value Potential for Near-Perfectly Competitive Markets

“…Cournot equilibrium with an infinite number of competitors tends to become perfect competition. However, stability of the equilibrium in such a conversion was questioned and analyzed by Puu (2008).…”