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An existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy

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  • Shirai, Koji
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    Abstract

    We establish an existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy. Instead of the traditional approach which depends on Kakutani's fixed point theorem, we employ the theories of aggregative games and best reply potential games. We show that, if there exists a representative consumer, under some conditions on preferences and production technologies, the profit maximization game is a (pseudo) best reply potential game. Hence, the existence of the equilibria is proved independently of the well known convex-valued assumption on the best responses. Although our assumptions result in the additive separability on a utility function of a representative consumer, the existence of increasing returns and indivisible productions can be allowed. In our model, it is shown that the game played by firms exhibits strategic substitutes whether the products of firms are substitutes or complements, and this plays an important role for the existence of the equilibria.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 6 (November)
    Pages: 1093-1102

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    Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1093-1102

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Monopolistic competition General equilibrium with imperfect competition Aggregative game Potential game Additive utility;

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    1. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
    2. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    3. John Roberts & Hugo Sonnenschein, 1976. "On the Foundations of the Theory of Monopolistic Competition," Discussion Papers 169, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Bloch, Francis & Ferrer, Helene, 2001. "Strategic complements and substitutes in bilateral oligopolies," Economics Letters, Elsevier, vol. 70(1), pages 83-87, January.
    5. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
    6. Egbert Dierker & Birgit Grodal, 1996. "The Price Normalization Problem in Imperfect Competition and the Objective of the Firm," Discussion Papers 96-05, University of Copenhagen. Department of Economics.
    7. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer, vol. 43(1), pages 45-66, April.
    8. Roy, Sunanda & Sabarwal, Tarun, 2005. "Monotone Comparative Statics for Games with Strategic Substitutes," MPRA Paper 4709, University Library of Munich, Germany, revised 04 Sep 2007.
    9. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    10. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    11. Camelia Bejan, 2008. "The objective of a privately owned firm under imperfect competition," Economic Theory, Springer, vol. 37(1), pages 99-118, October.
    12. FitzRoy, Felix R., 1974. "Monopolistic equilibrium, non-convexity and inverse demand," Journal of Economic Theory, Elsevier, vol. 7(1), pages 1-16, January.
    13. Bonanno, Giacomo, 1990. " General Equilibrium Theory with Imperfect Competition," Journal of Economic Surveys, Wiley Blackwell, vol. 4(4), pages 297-328.
    14. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
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