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Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem

  • Francesca Busetto
  • Giulio Codognato
  • Sayantan Ghosal

In this paper, in an exchange economy with atoms and an atomless part, we analyze the relationship between the set of the Cournot-Nash equilibrium allocations of a strategic market game and the set of the Walras equilibrium allocations of the exchange economy with which it is associated. In an example, we show that, even when atoms are countably infinite, Cournot-Nash equilibria yield different allocations from the Walras equilibrium allocations of the underlying exchange economy. We partially replicate the exchange economy by increasing the number of atoms without affecting the atomless part while ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market game associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

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File URL: http://economix.fr/pdf/dt/2012/WP_EcoX_2012-49.pdf
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Paper provided by University of Paris West - Nanterre la Défense, EconomiX in its series EconomiX Working Papers with number 2012-49.

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Length: 18 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:drm:wpaper:2012-49
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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. 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.
  3. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
  4. Okuno, Masahiro & Postlewaite, Andrew & Roberts, John, 1980. "Oligopoly and Competition in Large Markets," American Economic Review, American Economic Association, vol. 70(1), pages 22-31, March.
  5. 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.
  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. 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.
  8. 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.
  9. Sahi, Siddhartha & Yao, Shuntian, 1989. "The non-cooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 325-346, September.
  10. Novshek, William & Sonnenschein, Hugo., 1983. "General Equilibrium with Free Entry: A Synthetic Approach to the Theory of Perfect Competition," Working Papers 497, California Institute of Technology, Division of the Humanities and Social Sciences.
  11. Roberts, John & Sonnenschein, Hugo, 1977. "On the Foundations of the Theory of Monopolistic Competition," Econometrica, Econometric Society, vol. 45(1), pages 101-13, January.
  12. Mas-Colell, Andreu, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part I: Mixed strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 153-170, June.
  13. Roberts, Kevin, 1980. "The limit points of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 22(2), pages 256-278, April.
  14. Novshek, William & Sonnenschein, Hugo, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 171-187, June.
  15. 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.
  16. 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).
  17. 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.
  18. CODOGNATO, Giulio & GABSZEWICZ, Jean J., . "Cournot-Walras equilibria in markets with a continuum of traders," CORE Discussion Papers RP -1041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  19. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
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