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Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach

  • Ngo Van Long
  • Antoine Soubeyran

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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File URL: http://www.cirano.qc.ca/files/publications/99s-22.pdf
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Paper provided by CIRANO in its series CIRANO Working Papers with number 99s-22.

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Length: 9 pages
Date of creation: 01 Jun 1999
Date of revision:
Handle: RePEc:cir:cirwor:99s-22
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  1. 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.
  2. Szidarovszky, F & Yakowitz, S, 1977. "A New Proof of the Existence and Uniqueness of the Cournot Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 787-89, October.
  3. Kolstad, Charles D & Mathiesen, Lars, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 681-90, October.
  4. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Ngo Van Long & Antoine Soubeyran, 1999. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," CIRANO Working Papers 99s-13, CIRANO.
  6. Gaudet, G. & Salant, S.W., 1988. "Uniqueness Of Cournot Equilibrium: New Results From Old Methods," Cahiers de recherche 8818, Université Laval - Département d'économique.
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