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Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem

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  • Francesca Busetto
  • Giulio Codognato
  • Sayantan Ghosal

Abstract

In this paper, in an exchange economy with atoms and an atomless part, we analyze the relationship between the set of the Cournot-Nash equilibrium allocations of a strategic market game and the set of the Walras equilibrium allocations of the exchange economy with which it is associated. In an example, we show that, even when atoms are countably infinite, Cournot-Nash equilibria yield different allocations from the Walras equilibrium allocations of the underlying exchange economy. We partially replicate the exchange economy by increasing the number of atoms without affecting the atomless part while ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market game associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

Suggested Citation

  • Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2012. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem," EconomiX Working Papers 2012-49, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2012-49
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    More about this item

    Keywords

    Cournot-Nash equilibrium; strategic market games; limit theorem;
    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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