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Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach

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Author Info
Ngo Van Long ()
Antoine Soubeyran

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Abstract

We provide sufficient conditions for existence and uniqueness of a Cournot equilibrium. The contraction mapping approach is used. Equilibrium is characterized in terms of marginal costs. The result is useful for applications to two-stage games, where, in the first stage, firms incur costs to manipulate their marginal costs of production.

Cet article donne des conditions suffisantes pour l'existence et l'unicité de l'équilibre de Cournot. Notre résultat s'applique aux jeux de Cournot à deux étapes. Dans un premier temps, les firmes manipulent leurs coûts marginaux en choisissant un paramètre. Dans un deuxième temps, les firmes font la concurrence à la Cournot.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 99s-22.

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Date of creation: 01 Jun 1999
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Handle: RePEc:cir:cirwor:99s-22

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Related research
Keywords: Cournot equilibrium; existence; uniqueness; Équilibre de Cournot; existence; unicité;

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Find related papers by JEL classification:
L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
L23 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Organization of Production

References listed on IDEAS
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  1. Kolstad, Charles D & Mathiesen, Lars, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," Review of Economic Studies, Blackwell Publishing, vol. 54(4), pages 681-90, October. [Downloadable!] (restricted)
  2. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Blackwell Publishing, vol. 52(1), pages 85-98, January. [Downloadable!] (restricted)
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  3. Nishimura, Kazuo & Friedman, James, 1981. "Existence of Nash Equilibrium in n Person Games without Quasi-Concavity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 637-48, October. [Downloadable!] (restricted)
  4. Long, Ngo Van & Soubeyran, Antoine, 2001. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 505-33, May.
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  5. Gaudet, Gerard & Salant, Stephen W, 1991. "Uniqueness of Cournot Equilibrium: New Results from Old Methods," Review of Economic Studies, Blackwell Publishing, vol. 58(2), pages 399-404, April. [Downloadable!] (restricted)
    Other versions:
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Georg Götz, 2002. "Existence, Uniqueness, and Symmetry of Free-Entry Cournot Equilibrium: The Importance of Market Size and Technoligy Choice," Vienna Economics Papers 0214, University of Vienna, Department of Economics. [Downloadable!]
  2. Elvio Accinelli & Edgar Carrera, 2006. "Unicidad del equilibrio de Nash-Cournot con correspondencias de mejor respuesta contractivas," Documentos de Trabajo (working papers) 1506, Department of Economics - dECON. [Downloadable!]
  3. Ngo Van Long & Antoine Soubeyran, 2001. "Emission Taxes and Standards for an Asymmetric Oligopoly," CIRANO Working Papers 2001s-07, CIRANO. [Downloadable!]
  4. Juan Enrique Martinez-Legaz & Antoine Soubeyran, 2003. "Learning from Errors," UFAE and IAE Working Papers 557.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
  5. Pierre Fleckinger, 2007. "Collective Reputation and Market Structure: Regulating the Quality vs Quantity Trade-of," Working Papers hal-00243080_v1, HAL. [Downloadable!]
  6. Mason, Robin & Valentinyi, Akos, 2004. "Independence and Heterogeneity in Games of Incomplete Information," CEPR Discussion Papers 4177, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  7. Joan Canton & Antoine Soubeyran & Hubert Stahn, 2008. "Environmental Taxation and Vertical Cournot Oligopolies: How Eco-industries Matter," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 40(3), pages 369-382, July. [Downloadable!] (restricted)
  8. Seamus Hogan, 2009. "A New Sufficient Condition for Uniqueness in Continuous Games," Working Papers in Economics 09/06, University of Canterbury, Department of Economics. [Downloadable!]
  9. Ngo Van Long & Antoine Soubeyran, 2003. "A Theory of Favoritism under International Oligopoly," CIRANO Working Papers 2003s-15, CIRANO. [Downloadable!]
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