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Existence and optimality of oligopoly equilibria in linear exchange economies

Author

Listed:
  • Jean-Marc Bonnisseau

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Michael Florig

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a linear exchange economy and its successive replicas. We study the notion of Cournot-Walras equilibrium in which the consumers use the quantities of commodities put on the market as strategic variables. We prove that, generically, if the number of replications is large enough but finite, the competitive behaviour is an oligopoly equilibrium. Then, under a mild condition, which may be interpreted in terms of market regulation and/or market activity, we show that any sequence of oligopoly equilibria of successive replica economies converges to the Walrasian outcome and furthermore that every oligopoly equilibrium of large, but finite, replica is Pareto optimal. Consequently, under the same assumptions on the fundamentals of the economy, one has an asymptotic result on the convergence of oligopoly equilibria to the Walras equilibrium together with a generic existence result for the Cournot-Walras.

Suggested Citation

  • Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Post-Print halshs-00265698, HAL.
    • Handle: RePEc:hal:journl:halshs-00265698
    DOI: 10.1007/s00199-003-0363-6
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    References listed on IDEAS

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    1. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 727-741, November.
    2. M. Florig, 2004. "Equilibrium Correspondence of Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 97-109, January.
    3. Bottazzi, Jean-Marc & De Meyer, Bernard, 2003. "A market game for assets and taxed investors," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 657-675, July.
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    5. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    6. Champsaur, P. & Cornet, B., 1989. "Walrasian Exchange Processes," LIDAM Discussion Papers CORE 1989030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Bernard de Meyer & Jean-Marc Bottazzi, 2003. "A market game for assets and taxed investors," Post-Print hal-00259739, HAL.
    8. GABSZEWICZ, Jean & MICHEL, Philippe, 1992. "Oligopoly equilibria in exchange economies," LIDAM Discussion Papers CORE 1992047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Continuity and Uniqueness of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 237-263, May.
    10. Bottazzi, Jean-Marc, 1994. "Accessibility of Pareto optima by Walrasian exchange processes," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 585-603, November.
    11. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
    12. Michael Florig, 2003. "Arbitrary small indivisibilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 831-843, November.
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    Citations

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    Cited by:

    1. Godal Odd & Meland Frode, 2010. "Permit Markets, Seller Cartels and the Impact of Strategic Buyers," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-33, April.
    2. Busetto, Francesca & Codognato, Giulio & Ghosal, Syantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," Economic Research Papers 269786, University of Warwick - Department of Economics.
    3. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 727-741, November.
    4. Amani Kahloul & Rim Lahmandi-Ayed & Hejer Lasram & Didier Laussel, 2017. "Democracy and competition: Vertical differentiation and labor in a general equilibrium model," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(4), pages 860-874, August.
    5. Gaël Giraud & Céline Rochon, 2007. "Natural rate of unemployment and efficiency: a dynamic analysis with flexible prices and increasing returns," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00155739, HAL.
    6. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    7. Wang, Xu & Zhu, Lei & Liu, Pengfei, 2021. "Manipulation via endowments: Quantifying the influence of market power on the emission trading scheme," Energy Economics, Elsevier, vol. 103(C).
    8. Tunay I. Tunca, 2004. "Information Precision and Asymptotic Efficiency of Industrial Markets," Working Papers 04-11, NET Institute, revised Oct 2004.
    9. Odd Godal & Bjart Holtsmark, 2010. "International emissions trading with endogenous taxes," Discussion Papers 626, Statistics Norway, Research Department.
    10. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    11. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    12. Tunca, Tunay I., 2008. "Information precision and asymptotic efficiency of industrial markets," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 964-996, September.

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    More about this item

    Keywords

    Imperfect competition; Oligopoly equilibrium; Pareto optimum; Linear utility functions; Replication.; Replication;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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