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Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities

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  • Busetto, Francesca
  • Codognato, Giulio
  • Ghosal, Sayantan
  • Julien, Ludovic
  • Tonin, Simone

Abstract

We show the existence of a Cournot–Nash equilibrium for a mixed version of the Shapley window model, where large traders are represented as atoms and small traders are represented by an atomless part. Previous existence theorems for the Shapley window model, provided by Sahi and Yao (1989) in the case of economies with a finite number of traders and by Busetto et al. (2011) in the case of mixed exchange economies, are essentially based on the assumption that there are at least two atoms with strictly positive endowments and indifference curves contained in the strict interior of the commodity space. Our result does not require this restriction. It relies on the characteristics of the atomless part of the economy and exploits the fact that traders belonging to the atomless part have an endogenous “Walrasian” behavior.

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  • Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Julien, Ludovic & Tonin, Simone, 2018. "Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 478-485.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:478-485
    DOI: 10.1016/j.geb.2017.01.013
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    1. 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.
    2. 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.
    3. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    4. 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.
    5. Maria Gabriella Graziano & Marialaura Pesce & Niccolo Urbinati, 2023. "The Equitable Bargaining Set," CSEF Working Papers 676, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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    More about this item

    Keywords

    Shapley window model; Atoms; Atomless part; Cournot–Nash equilibrium;
    All these keywords.

    JEL classification:

    • 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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