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Noncooperative Oligopoly in Markets with a Continuum of Traders

  • 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)

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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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
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Handle: RePEc:wrk:warwec:866
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  1. CODOGNATO, Giulio & GHOSAL, Sayantan, . "Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices," CORE Discussion Papers RP 1461, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. d'Aspremont, Claude & Dos Santos Ferreira, Rodolphe & Gerard-Varet, Louis-Andre, 1997. "General Equilibrium Concepts under Imperfect Competition: A Cournotian Approach," Journal of Economic Theory, Elsevier, vol. 73(1), pages 199-230, March.
  3. Masahiro Okuno, 1977. "Oligopoly and Competition in Large Markets," Discussion Papers 305, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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).
  5. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
  6. 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.
  7. repec:cor:louvrp:-1265 is not listed on IDEAS
  8. Codognato, Giulio & Gabszewicz, Jean J, 1993. "Cournot-Walras Equilibria in Markets with a Continuum of Traders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(3), pages 453-64, July.
  9. Roberts, Kevin, 1980. "The limit points of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 22(2), pages 256-278, April.
  10. 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.
  11. Amir, Rabah & Sahi, Siddharta & Shubik, Martin & Yao, Shuntian, 1990. "A strategic market game with complete markets," Journal of Economic Theory, Elsevier, vol. 51(1), pages 126-143, June.
  12. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
  13. Postlewaite, A & Schmeidler, David, 1978. "Approximate Efficiency of Non-Walrasian Nash Equilibria," Econometrica, Econometric Society, vol. 46(1), pages 127-35, January.
  14. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265698, HAL.
  15. Lahmandi-Ayed, R, 1996. "Oligopoly Equilibria in Exchange Economies : Limit Theorems," Papiers d'Economie Mathématique et Applications 96.07, Université Panthéon-Sorbonne (Paris 1).
  16. 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.
  17. Benyamin Shitovitz, 1997. "A comparison between the core and the monopoly solutions in a mixed exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 559-563.
  18. 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.
  19. 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.
  20. 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.
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