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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
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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    1. Bloch, Francis & Ferrer, Helene, 2001. "Strategic complements and substitutes in bilateral oligopolies," Economics Letters, Elsevier, vol. 70(1), pages 83-87, January.
    2. Birgit Grodal & Egbert Dierker, 1999. "The price normalization problem in imperfect competition and the objective of the firm," Economic Theory, Springer, vol. 14(2), pages 257-284.
    3. Camelia Bejan, 2008. "The objective of a privately owned firm under imperfect competition," Economic Theory, Springer, vol. 37(1), pages 99-118, October.
    4. Roy, Sunanda & Sabarwal, Tarun, 2010. "Monotone comparative statics for games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 793-806, September.
    5. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    6. ROBERTS, John & SONNENSCHEIN, Hugo, . "On the foundations of the theory of monopolistic competition," CORE Discussion Papers RP 296, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
    8. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
    9. FitzRoy, Felix R., 1974. "Monopolistic equilibrium, non-convexity and inverse demand," Journal of Economic Theory, Elsevier, vol. 7(1), pages 1-16, January.
    10. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer, vol. 43(1), pages 45-66, April.
    11. 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).
    12. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    13. 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.
    14. Bonanno, Giacomo, 1990. " General Equilibrium Theory with Imperfect Competition," Journal of Economic Surveys, Wiley Blackwell, vol. 4(4), pages 297-328.
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