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Atomic Cournotian Traders May Be Walrasian

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  • Codognato, Giulio
  • Ghosal, Sayantan
  • Tonin, Simone

Abstract

In a bilateral oligopoly, with large traders, represented as atoms, and small traders, represented by an atomless part, when is there a non-empty intersection between the sets of Walras and Cournot-Nash allocations? Using a two commodity version of the Shapley window model, we show that a necessary and sufficient condition for a Cournot- Nash allocation to be a Walras allocation is that all atoms demand a null amount of one of the two commodities. We provide two examples which show that this characterization holds non-vacuously. When our condition fails to hold, we also confirm, through some examples, the result obtained by Okuno, Postlewaite, and Roberts (1980): small traders always have a negligible influence on prices, while the large traders keep their strategic power even when their behavior turns out to be Walrasian in the cooperative framework considered by Gabszewicz and Mertens (1971) and Shitovitz (1973).

Suggested Citation

  • Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2014. "Atomic Cournotian Traders May Be Walrasian," SIRE Discussion Papers 2014-024, Scottish Institute for Research in Economics (SIRE).
  • Handle: RePEc:edn:sirdps:580
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    File URL: http://hdl.handle.net/10943/580
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    References listed on IDEAS

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    1. Gabszewicz, Jean Jaskold & Mertens, Jean-Francois, 1971. "An Equivalence Theorem for the Core of an Economy Whose Atoms Are Not 'Too' Big," Econometrica, Econometric Society, vol. 39(5), pages 713-721, September.
    2. Amir, Rabah & Bloch, Francis, 2009. "Comparative statics in a simple class of strategic market games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 7-24, January.
    3. Bloch, Francis & Ghosal, Sayantan, 1997. "Stable Trading Structures in Bilateral Oligopolies," Journal of Economic Theory, Elsevier, vol. 74(2), pages 368-384, June.
    4. Bloch, Francis & Ferrer, Helene, 2001. "Trade Fragmentation and Coordination in Strategic Market Games," Journal of Economic Theory, Elsevier, vol. 101(1), pages 301-316, November.
    5. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, number 9890, October.
    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. 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.
    8. 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.
    9. Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
    10. 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.
    11. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
    12. 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).
    13. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    14. 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.
    15. 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.
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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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