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Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach

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  • Ngo Van Long
  • Antoine Soubeyran

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.

Suggested Citation

  • Ngo Van Long & Antoine Soubeyran, 1999. "Existence and Uniqueness of Cournot Equilibrium: A Contraction Mapping Approach," CIRANO Working Papers 99s-22, CIRANO.
  • Handle: RePEc:cir:cirwor:99s-22
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    References listed on IDEAS

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    1. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
    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 787-789, October.
    3. Charles D. Kolstad & Lars Mathiesen, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 681-690.
    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 505-533, May.
    5. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 399-404.
    6. 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 637-648, October.
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    Cited by:

    1. 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.
    2. Van Long, Ngo, 2013. "The theory of contests: A unified model and review of the literature," European Journal of Political Economy, Elsevier, vol. 32(C), pages 161-181.
    3. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2013. "The empirical content of Cournot competition," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1552-1581.
    4. Joan Canton & Antoine Soubeyran & Hubert Stahn, 2008. "Environmental Taxation and Vertical Cournot Oligopolies: How Eco-industries Matter," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 40(3), pages 369-382, July.
    5. Ngo Van Long & Antoine Soubeyran, 2003. "A Theory of Favoritism under International Oligopoly," CIRANO Working Papers 2003s-15, CIRANO.
    6. 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 505-533, May.
    7. Arye Hillman & Ngo Van Long, 2017. "The social cost of contestable benefits," CIRANO Working Papers 2017s-11, CIRANO.
    8. Luckraz, Shravan, 2011. "R&D games in a Cournot duopoly with isoelastic demand functions: A comment," Economic Modelling, Elsevier, vol. 28(6), pages 2873-2876.
    9. Ngo Long & Antoine Soubeyran, 2005. "Selective penalization of polluters: an inf-convolution approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(2), pages 421-454, February.
    10. 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.
    11. Arye L. Hillman & Ngo Van Long, 2017. "Rent Seeking: The Social Cost of Contestable Benefits," CESifo Working Paper Series 6462, CESifo Group Munich.
    12. Max Albert & Andreas Hildenbrand, 2012. "Industrial organization in the laboratory," MAGKS Papers on Economics 201205, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    13. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    14. Ngo Van Long & Antoine Soubeyran, 2001. "Emission Taxes and Standards for an Asymmetric Oligopoly," CIRANO Working Papers 2001s-07, CIRANO.
    15. 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).
    16. Mason, Robin & Valentinyi, Ã kos, 2007. "The existence and uniqueness of monotone pure strategy equilibrium in Bayesian games," Discussion Paper Series In Economics And Econometrics 0710, Economics Division, School of Social Sciences, University of Southampton.
    17. Pierre Fleckinger, 2007. "Collective Reputation and Market Structure: Regulating the Quality vs Quantity Trade-of," Working Papers hal-00243080, HAL.
    18. Jinji, Naoto, 2014. "Comparative statics for oligopoly: A generalized result," Economics Letters, Elsevier, vol. 124(1), pages 79-82.
    19. Yukako Ono, 2000. "Outsourcing Business Service and the Scope of Local Markets," Working Papers 00-14, Center for Economic Studies, U.S. Census Bureau.
    20. Ngo Van Long & Antoine Soubeyran, 2000. "Permis de pollution et oligopole asymétrique," Économie et Prévision, Programme National Persée, vol. 143(2), pages 83-89.
    21. Mason, Robin & Valentinyi, Akos, 2004. "Independence and Heterogeneity in Games of Incomplete Information," CEPR Discussion Papers 4177, C.E.P.R. Discussion Papers.
    22. Seamus Hogan, 2009. "A New Sufficient Condition for Uniqueness in Continuous Games," Working Papers in Economics 09/06, University of Canterbury, Department of Economics and Finance.
    23. repec:elg:eechap:15325_3 is not listed on IDEAS

    More about this item

    Keywords

    Cournot equilibrium; existence; uniqueness; Équilibre de Cournot; existence; unicité;

    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

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