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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)

  • Giulio Codognato

    (Università degli Studi di Udine
    Economix, UPL, Univ Paris Nanterre, CNRS)

  • Sayantan Ghosal

    (University of Glasgow)

  • Ludovic Julien

    (Economix, UPL, Univ Paris Nanterre, CNRS)

  • Simone Tonin

    (Università degli Studi di Udine)

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 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.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:4:d:10.1007_s00182-020-00719-z
    DOI: 10.1007/s00182-020-00719-z
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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. 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.
    3. 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.
    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.

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    More about this item

    Keywords

    Bilateral oligopoly; Cournot–Nash equilibrium; Pareto optimality;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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