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Existence and optimality of oligopoly equilibria in linear exchange economies


  • Jean-Marc Bonnisseau
  • Michael Florig


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.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:22:y:2003:i:4:p:727-741 DOI: 10.1007/s00199-003-0363-6

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    References listed on IDEAS

    1. 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.
    2. Monique Florenzano & Emma Moreno-García, 2001. "Linear exchange economies with a continuum of agents," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(4), pages 253-272.
    3. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    4. Champsaur, P. & Cornet, B., 1989. "Walrasian Exchange Processes," CORE Discussion Papers 1989030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. GABSZEWICZ, Jean & MICHEL, Philippe, 1992. "Oligopoly equilibria in exchange economies," CORE Discussion Papers 1992047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Bottazzi, Jean-Marc, 1994. "Accessibility of Pareto optima by Walrasian exchange processes," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 585-603, November.
    7. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
    8. 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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    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, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    3. Tunay I. Tunca, 2004. "Information Precision and Asymptotic Efficiency of Industrial Markets," Working Papers 04-11, NET Institute, revised Oct 2004.
    4. Odd Godal & Bjart Holtsmark, 2010. "International emissions trading with endogenous taxes," Discussion Papers 626, Statistics Norway, Research Department.
    5. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    6. 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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