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

  • Shirai, Koji
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    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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    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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    9. BLOCH, Francis & FERRER, Hélène, 1998. "Strategic complements and substitutes in bilateral oligopolies," CORE Discussion Papers 1998030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. 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.
    11. Camelia Bejan, 2008. "The objective of a privately owned firm under imperfect competition," Economic Theory, Springer, vol. 37(1), pages 99-118, October.
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    13. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    14. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
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