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Free entry equilibria with positive profits: A unified approach to quantity and price competition games


  • Rodolphe Dos Santos Ferreira

    (BETA - Bureau d'Économie Théorique et Appliquée - INRA - Institut National de la Recherche Agronomique - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique)

  • Frédéric Dufourt

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)


Free entry equilibria are usually characterized by the zero profit condition. We plead instead for a strict application of theNash equilibriumconcept to a symmetric simultaneous game played by actual and potential entrants, producing under decreasing average cost. Equilibrium is then typically indeterminate, with a number of active firms varying between an upper bound imposed by profitability and a lower bound required by sustainability. We use a canonical model with strategies represented by prices, although covering standard regimes of quantity and price competition, to show that in equilibrium the critical (profit maximizing) price must lie between the break-even and the limit prices.

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  • Rodolphe Dos Santos Ferreira & Frédéric Dufourt, 2007. "Free entry equilibria with positive profits: A unified approach to quantity and price competition games," Post-Print halshs-00796163, HAL.
  • Handle: RePEc:hal:journl:halshs-00796163
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    References listed on IDEAS

    1. Claude d'Aspremont & Rodolphe Dos Santos Ferreira & Louis-André Gérard-Varet, 2007. "Competition For Market Share Or For Market Size: Oligopolistic Equilibria With Varying Competitive Toughness," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 761-784, August.
    2. Weitzman, Martin L, 1982. "Increasing Returns and the Foundations of Unemployment Theory," Economic Journal, Royal Economic Society, vol. 92(368), pages 787-804, December.
    3. Baumol, William J, 1982. "Contestable Markets: An Uprising in the Theory of Industry Structure," American Economic Review, American Economic Association, vol. 72(1), pages 1-15, March.
    4. d'Aspremont, Claude & Dos Santos Ferreira, Rodolphe & Gerard-Varet, Louis-Andre, 1996. "On the Dixit-Stiglitz Model of Monopolistic Competition," American Economic Review, American Economic Association, vol. 86(3), pages 623-629, June.
    5. Claude D’Aspremont & Rodolphe Dos Santos Ferreira & Louis-Andre Gerard-Varet, 2000. "Contestability and the Indeterminacy of Free-Entry Equilibria," The Japanese Economic Review, Japanese Economic Association, vol. 51(1), pages 72-83, March.
    6. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, Oxford University Press, vol. 103(3), pages 441-463.
    7. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    8. Dos Santos Ferreira, Rodolphe & Dufourt, Frederic, 2006. "Free entry and business cycles under the influence of animal spirits," Journal of Monetary Economics, Elsevier, vol. 53(2), pages 311-328, March.
    9. Franco Modigliani, 1958. "New Developments on the Oligopoly Front," Journal of Political Economy, University of Chicago Press, vol. 66, pages 215-215.
    10. Makoto Yano, 2006. "A price competition game under free entry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 395-414, October.
    11. William Novshek, 1980. "Cournot Equilibrium with Free Entry," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 473-486.
    12. Corchon, Luis C. & Fradera, Isabel, 2002. "Comparative statics in Cournot free entry equilibrium," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 155-168, November.
    13. Georg Götz, 2005. "Market Size, Technology Choice, and the Existence of Free-Entry Cournot Equilibrium," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 161(3), pages 503-503, September.
    14. Brock, William A, 1983. "Contestable Markets and the Theory of Industry Structure: A Review Article," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 1055-1066, December.
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    Cited by:

    1. Rodolphe Dos Santos Ferreira & Frédéric Dufourt, 2013. "On Stabilization Policy in Sunspot-Driven Oligopolistic Economies," AMSE Working Papers 1337, Aix-Marseille School of Economics, Marseille, France, revised 30 Jun 2013.
    2. Dos Santos Ferreira, Rodolphe & Lloyd-Braga, Teresa, 2008. "Business cycles with free entry ruled by animal spirits," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3502-3519, November.
    3. Makoto Yano, 2009. "The Foundation Of Market Quality Economics," The Japanese Economic Review, Japanese Economic Association, vol. 60(1), pages 1-32.
    4. Germán Coloma, 2010. "El número óptimo de empresas bajo competencia de Bertrand," Estudios de Economia, University of Chile, Department of Economics, vol. 37(2 Year 20), pages 189-205, December.
    5. Takashi Komatsubara, 2008. "Equilibrium Selection In The Yano Model Of Price Leadership," Pacific Economic Review, Wiley Blackwell, vol. 13(5), pages 649-655, December.


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