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Existence and Optimality of Cournot-Nash Equilibria in a Bilateral Oligopoly with Atoms and an Atomless Part

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  • Francesca Busetto
  • Giulio Codognato
  • Sayantan Ghosal
  • Ludovic A. Julien
  • Simone Tonin

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 (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, 2018. "Existence and Optimality of Cournot-Nash Equilibria in a Bilateral Oligopoly with Atoms and an Atomless Part," EconomiX Working Papers 2018-10, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2018-10
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    Cited by:

    1. Ludovic A. Julien & Gagnie Pascal Yebarth, 2024. "Pareto-Optimal Taxation Mechanism in Noncooperative Strategic Bilateral Exchange," EconomiX Working Papers 2024-19, University of Paris Nanterre, EconomiX.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

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    More about this item

    Keywords

    Shapley window model; Atoms; Atomless part; Cournot–Nash equilibrium; Optimality;
    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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