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Noncooperative oligopoly in markets with a continuum of traders: a limit theorem a la Cournot

Listed author(s):
  • Francesca Busetto
  • Giulio Codognato
  • Sayantan Ghosal

In this paper, we consider an exchange economy `a la Shitovitz (1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley and known as the Shapley window model. We analyze the relationship between the set of the Cournot-Nash equilibrium allocations of the strategic market game and the Walras equilibrium allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably infinite, any Cournot-Nash equilibrium allocation of the game is not a Walras equilibrium of the underlying exchange economy. Accordingly, in the original spirit of Cournot (1838), we partially replicate the mixed exchange economy by increasing the number of atoms, without affecting the atomless part, and ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market games associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

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Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2014_01.

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Handle: RePEc:gla:glaewp:2014_01
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  1. 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.
  2. d'ASPREMONT, C. & DOS SANTOS FERREIRA, R. & ÉRARD-VARET, L.-A., "undated". "General equilibrium concepts under imperfect competition: a Cournotian approach," CORE Discussion Papers RP 1259, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. 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.
  4. CODOGNATO, Giulio & GABSZEWICZ, Jean J., "undated". "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).
  5. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
  6. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2013. "Three Models of Noncooperative Oligopoly in Markets with a Continuum of Traders," Recherches économiques de Louvain, De Boeck Université, vol. 79(4), pages 15-32.
  7. 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 937-968, October.
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  9. Charles R. Frank, 1965. "Entry in a Cournot Market," Review of Economic Studies, Oxford University Press, vol. 32(3), pages 245-250.
  10. 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.
  11. 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.
  12. Novshek, William & Sonnenschein, Hugo, 1987. "General Equilibrium with Free Entry: A Synthetic Approach to the Theory of Perfect Competition," Journal of Economic Literature, American Economic Association, vol. 25(3), pages 1281-1306, September.
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  16. 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.
  17. 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.
  18. Codognato, Giulio, 2000. "Cournot-Nash Equilibria in Limit Exchange Economies with Complete Markets: A Comparison between Two Models," Games and Economic Behavior, Elsevier, vol. 31(1), pages 136-146, April.
  19. 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.
  20. R. J. Ruffin, 1971. "Cournot Oligopoly and Competitive Behaviour," Review of Economic Studies, Oxford University Press, vol. 38(4), pages 493-502.
  21. 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.
  22. Martin Shubik & Jingang Zhao, 1990. "A Strategic Market Game of a Finite Economy with a Mutual Bank," Cowles Foundation Discussion Papers 961, Cowles Foundation for Research in Economics, Yale University.
  23. 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.
  24. Francesca BUSETTO & Giulio CODOGNATO & Sayantan GHOSSAL, 2013. "Three Models of Noncooperative Oligopoly in Markets with a Continuum of Traders," Discussion Papers (REL - Recherches Economiques de Louvain) 2013041, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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