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Noncooperative Oligopoly in Markets with a Continuum of Traders

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  • Busetto, Francesca

    (Dipartimento di Scienze Economiche, Universitµa degli Studi di Udine)

  • Codognato, Giulio

    (Dipartimento di Scienze Economiche, Universitµa degli Studi di Udine)

  • Ghosal, Sayantan

    (Department of Economics, University of Warwick)

Abstract

In this paper, we study three prototypical models of noncooperative oligopoly in markets with a continuum of traders : the model of Cournot-Walras equilibrium of Codognato and Gabszewicz (1991), the model of Cournot-Nash equilibrium of Lloyd S. Shapley, and the model of Cournot-Walras equilibrium of Busetto et al. (2008). We argue that these models are all distinct and only the Shapley's model with a continuum of traders and atoms gives an endogenous explanation of the perfectly and imperfectly competitive behavior of agents in a one-stage setting. For this model, we prove a theorem of existence of a Cournot-Nash equilibrium.

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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 866.

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Length: 32 pages
Date of creation: 2008
Date of revision:
Handle: RePEc:wrk:warwec:866

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  1. D'Aspremont, C. & Dos Santos Ferreira, R. & Gerard-Varet, L.A., 1992. "General Equilibrium Concepts Under Imperfect Competition: A Cournotien Approach," G.R.E.Q.A.M. 92a03, Universite Aix-Marseille III.
  2. Rabah Amir & Siddhartha Sahi & Martin Shubik, 1986. "A Strategic Market Game with Complete Markets," Cowles Foundation Discussion Papers 814R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  3. John Roberts & Hugo Sonnenschein, 1976. "On the Foundations of the Theory of Monopolistic Competition," Discussion Papers 169, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Postlewaite, A & Schmeidler, David, 1978. "Approximate Efficiency of Non-Walrasian Nash Equilibria," Econometrica, Econometric Society, vol. 46(1), pages 127-35, January.
  5. Peck, James & Shell, Karl & Spear, Stephen E., 1992. "The market game: existence and structure of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 271-299.
  6. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
  7. 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).
  8. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer, vol. 22(4), pages 727-741, November.
  9. Benyamin Shitovitz, 1997. "A comparison between the core and the monopoly solutions in a mixed exchange economy," Economic Theory, Springer, vol. 10(3), pages 559-563.
  10. Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
  11. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
  12. Masahiro Okuno, 1977. "Oligopoly and Competition in Large Markets," Discussion Papers 305, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Codognato, Giulio & Ghosal, Sayantan, 2000. "Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 39-53, August.
  14. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 837, University of Warwick, Department of Economics.
  15. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-68, October.
  16. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
  17. Roberts, Kevin, 1980. "The limit points of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 22(2), pages 256-278, April.
  18. Lahmandi-Ayed, R, 1996. "Oligopoly Equilibria in Exchange Economies : Limit Theorems," Papiers d'Economie Mathématique et Applications 96.07, Université Panthéon-Sorbonne (Paris 1).
  19. Codognato, Giulio & Gabszewicz, Jean J, 1993. "Cournot-Walras Equilibria in Markets with a Continuum of Traders," Economic Theory, Springer, vol. 3(3), pages 453-64, July.
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Cited by:
  1. David Mayer-Foulkes, 2011. "Vulnerable Markets," DEGIT Conference Papers c016_040, DEGIT, Dynamics, Economic Growth, and International Trade.
  2. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2012. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem," The Warwick Economics Research Paper Series (TWERPS) 994, University of Warwick, Department of Economics.

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