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Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem

Author

Listed:
  • Francesca Busetto
  • Giulio Codognato

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Sayantan Ghosal
  • Ludovic A. Julien

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Damiano Turchet

Abstract

We consider a mixed version of the Shapley window model, where large traders are represented as atoms and small traders are represented by an atomless part. Our main theorem shows that any sequence of Cournot-Nash allocations of the strategic market games associated with the partial replications of the exchange economy has a limit point for each trader and that the assignment determined by these limit points is a Walrasian allocation of the original economy. Instead of relying on restrictive assumptions on the characteristics of atoms, as in Busetto et al. (2017), our limit theorem relies on the characteristics of agents in the atomless part and their endogenously price-taking behavior.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:wpaper:hal-04194965
    Note: View the original document on HAL open archive server: https://hal.science/hal-04194965
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    References listed on IDEAS

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    1. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    2. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2017. "Asymptotic equivalence between Cournot–Nash and Walras equilibria in exchange economies with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 975-990, November.
    3. 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.
    4. 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.
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    More about this item

    Keywords

    Cournot-Nash equilibrium; Walras equilibrium; Asymptotic equivalence;
    All these keywords.

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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