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Atomic Cournotian traders may be Walrasian

Author

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  • Giulio Codognato
  • Sayantan Ghosal
  • Simone Tonin

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 exam- ples 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

  • Giulio Codognato & Sayantan Ghosal & Simone Tonin, 2014. "Atomic Cournotian traders may be Walrasian," Working Papers 2014_12, Business School - Economics, University of Glasgow.
    • Handle: RePEc:gla:glaewp:2014_12
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    References listed on IDEAS

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    Cited by:

    1. Francesca Busetto & Giulio Codognato & Giorgia Pavan & Simone Tonin, 2023. "Cournotian duopolistic firms may be Walrasian: a case in the Gabszewicz and Vial model," Journal of Economics, Springer, vol. 140(2), pages 121-140, October.
    2. Andrés Carvajal, 2018. "Arbitrage pricing in non-Walrasian financial markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 951-978, December.
    3. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic Julien & Simone Tonin, 2020. "Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 933-951, December.
    4. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic A. Julien & Damiano Turchet, 2023. "Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem," Working Papers hal-04194965, HAL.
    5. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    6. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2020. "Atomic Leontievian Cournotian traders are always Walrasian," Games and Economic Behavior, Elsevier, vol. 122(C), pages 318-327.

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    More about this item

    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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