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Existence and optimality of Cournot-Nash equilibria in a bilateral oligopoly with atoms and an atomless part

Author

Listed:
  • Francesca Busetto

    (Università degli Studi di Udine - University of Udine [Italie])

  • Giulio Codognato

    (Università degli Studi di Udine - University of Udine [Italie], EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Sayantan Ghosal

    (Adam Smith Business School - University of Glasgow)

  • Ludovic A. Julien

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

  • Simone Tonin

    (Università degli Studi di Udine - University of Udine [Italie])

Abstract

We consider a bilateral oligopoly version of the Shapley window model with large traders, represented as atoms, and small traders, represented by an atomless part. For this model, we provide a general existence proof of a Cournot-Nash equilibrium that allows one of the two commodities to be held only by atoms. Then, we show, using a corollary proved by Shitovitz (Econometrica 41:467-501, 1973), that a Cournot-Nash allocation is Pareto optimal if and only if it is a Walras allocation.

Suggested Citation

  • Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic A. Julien & Simone Tonin, 2020. "Existence and optimality of Cournot-Nash equilibria in a bilateral oligopoly with atoms and an atomless part," Post-Print hal-02531404, HAL.
    • Handle: RePEc:hal:journl:hal-02531404
    DOI: 10.1007/s00182-020-00719-z
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    Cited by:

    1. Gagnie Pascal Yebarth, 2025. "On Taxation Policy in Strategic Bilateral Exchange: A review," EconomiX Working Papers 2025-34, University of Paris Nanterre, EconomiX.
    2. Ludovic A. Julien & Gagnie Pascal Yebarth, 2024. "Pareto-Optimal Taxation Mechanism in Noncooperative Strategic Bilateral Exchange," Working Papers hal-04604299, HAL.
    3. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Damiano Turchet, 2023. "On the foundation of monopoly in bilateral exchange," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1261-1290, December.
    4. 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.
    5. 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.
    6. Ludovic A. Julien, 2024. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 325-371, June.

    More about this item

    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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