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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 - CNRS - Université Louis Pasteur - Strasbourg I)

  • Frédéric Dufourt


    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université Paul Cézanne - Aix-Marseille 3 - Université de la Méditerranée - Aix-Marseille 2 - EHESS - École des hautes études en sciences sociales - CNRS - AMU - Aix-Marseille Université)

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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Paper provided by HAL in its series Post-Print with number halshs-00796163.

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Date of creation: 01 May 2007
Date of revision:
Publication status: Published in International Journal of Economic Theory, Wiley, 2007, 3 (2), pp.75-94
Handle: RePEc:hal:journl:halshs-00796163
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  1. d'ASPREMONT, C. & DOS SANTOS FERREIRA, R. & GÉRARD-VARET, L.-A., . "On the Dixit-Stiglitz model of monopolistic competition," CORE Discussion Papers RP 1211, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. William Novshek, 1980. "Cournot Equilibrium with Free Entry," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 473-486.
  3. d’ASPREMONT, Claude & DOS SANTOS FERREIRA, Rodolphe & GERARD-VARET, Louis-André, 1997. "Contestability and the indeterminacy of free entry equilibria," CORE Discussion Papers 1997073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Franco Modigliani, 1958. "New Developments on the Oligopoly Front," Journal of Political Economy, University of Chicago Press, vol. 66, pages 215.
  5. 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 1055-66, December.
  6. 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-, September.
  7. Corchon, Luis C. & Fradera, Isabel, 2002. "Comparative statics in Cournot free entry equilibrium," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 155-168, November.
  8. 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.
  9. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
  10. Rodolphe Dos Santos Ferreira & Frederic Dufourt, 2006. "Free entry and business cycles under the influence of animal spirits," Post-Print halshs-00789030, HAL.
  11. d'ASPREMONT, Claude & DOS SANTOS-FERREIRA, Rodolphe & GÉRARD-VARET, Louis-André, 2003. "Competition for market share or for market size: oligopolistic equilibria with varying competitive toughness," CORE Discussion Papers 2003010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Makoto Yano, 2006. "A price competition game under free entry," Economic Theory, Springer, vol. 29(2), pages 395-414, October.
  13. Weitzman, Martin L, 1982. "Increasing Returns and the Foundations of Unemployment Theory," Economic Journal, Royal Economic Society, vol. 92(368), pages 787-804, December.
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