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Asymptotic equivalence between Cournot–Nash and Walras equilibria in exchange economies with atoms and an atomless part

Author

Listed:
  • Francesca Busetto

    (Università degli Studi di Udine)

  • Giulio Codognato

    (Università degli Studi di Udine
    Université Paris Ouest-Nanterre La Défense)

  • Sayantan Ghosal

    (University of Glasgow)

Abstract

In this paper, we consider an exchange economy à la Shitovitz (Econometrica 41:467–501, 1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley, known as the Shapley window model. We analyze the relationship between the set of the Cournot–Nash allocations of the strategic market game and the Walras allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably infinite, any Cournot–Nash allocation of the game is not a Walras allocation of the underlying exchange economy. Accordingly, in the original spirit of Cournot (Recherches sur les principes mathématiques de la théorie des richesses. Hachette, Paris, 1838), we partially replicate the mixed exchange economy by increasing the number of atoms, without affecting the atomless part, and ensuring that the measure space of agents remains finite. 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.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0566-x
    DOI: 10.1007/s00182-017-0566-x
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    References listed on IDEAS

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    Cited by:

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    2. 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

    Cournot-Nash equilibrium; Walras equilibrium; Asymptotic equivalence;
    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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