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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
  • 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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    References listed on IDEAS

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    4. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, number 9890, October.
    5. Dubey, Pradeep & Mas-Colell, Andreau & Shubik, Martin, 1980. "Efficiency properties of strategies market games: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 22(2), pages 339-362, April.
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    7. Sahi, Siddhartha & Yao, Shuntian, 1989. "The non-cooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 325-346, September.
    8. Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
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    More about this item

    Keywords

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

    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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