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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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Article provided by Springer in its journal Economic Theory.

Volume (Year): 22 (2003)
Issue (Month): 4 (November)
Pages: 727-741

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Handle: RePEc:spr:joecth:v:22:y:2003:i:4:p:727-741
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  1. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
  2. Michael Florig, 2003. "Arbitrary small indivisibilities," Economic Theory, Springer, vol. 22(4), pages 831-843, November.
  3. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
  4. Monique Florenzano & Emma Moreno-García, 2001. "Linear exchange economies with a continuum of agents," Spanish Economic Review, Springer, vol. 3(4), pages 253-272.
  5. Gabszewicz, J.J. & Michel, P., . "Oligopoly equilibrium in exchange economies," CORE Discussion Papers RP 1265, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Bernard De Meyer & Jean-Marc Bottazzi, 2003. "A market game for assets and taxed investors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00259739, HAL.
  7. Bottazzi, Jean-Marc, 1994. "Accessibility of Pareto optima by Walrasian exchange processes," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 585-603, November.
  8. Champsaur, P. & Cornet, B., 1989. "Walrasian Exchange Processes," CORE Discussion Papers 1989030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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