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Noncooperative Oligopoly in Markets with a Cobb-Douglas Continuum of Traders

Author

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  • Giulio Codognato
  • Ludovic A. Julien

Abstract

In this paper, we reconsider two models of noncooperative oligopoly in general equilibrium proposed by Busetto et al. ((2008), (2011)): a version of the Shapley?s window model for mixed exchange economies à la Shitovitz and its reformulation à la Cournot-Walras. We introduce the assumption that preferences of the traders belonging to the atomless part are represented by Cobb-Douglas utility functions. This assumption permits us to prove the existence of a Cournot-Nash equilibrium of the Shapley?s window model - called Cobb-Douglas-Cournot-Nash equilibrium - without introducing further assumptions on atoms? endowments and preferences previously used by Busetto et al. (2011). Then, we show that the set of the Cobb-Douglas-Cournot-Nash equilibrium allocations coincides with the set of the Cournot-Walras equilibrium allocations. JEL Classification: C72, D51.

Suggested Citation

  • Giulio Codognato & Ludovic A. Julien, 2013. "Noncooperative Oligopoly in Markets with a Cobb-Douglas Continuum of Traders," Recherches économiques de Louvain, De Boeck Université, vol. 79(4), pages 75-88.
    • Handle: RePEc:cai:reldbu:rel_794_0075
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    Cited by:

    1. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Julien, Ludovic & Tonin, Simone, 2018. "Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 478-485.
    2. Roy H Grieve, 2013. "An issue with own-rates: Keynes borrows from Sraffa , Sraffa criticises Keynes, and present-day commentators get hold of the wrong end of the stick," Working Papers 1319, University of Strathclyde Business School, Department of Economics.
    3. 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.
    4. Alex Dickson, 2013. "On Cobb-Douglas Preferences in Bilateral Oligopoly," Recherches économiques de Louvain, De Boeck Université, vol. 79(4), pages 89-110.
    5. S. S. Askar & A. Al-khedhairi, 2019. "Cournot Duopoly Games: Models and Investigations," Mathematics, MDPI, vol. 7(11), pages 1-15, November.

    More about this item

    Keywords

    strategic market games; noncooperative oligopoly; atoms; atomless part;
    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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