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Competition for market share or for market size: oligopolistic equilibria with varying competitive toughness

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  • d'ASPREMONT, Claude
  • DOS SANTOS-FERREIRA, Rodolphe
  • GÉRARD-VARET, Louis-André

Abstract

We propose a comprehensive concept of oligopolistic equilibrium, allowing for a parametrized continuum of competition regimes, with each firm setting simultaneously both its price and its quantity and facing two constraints: one relative to its share ofthe market, the other relative to the size of the market. The type of solution (i.e. the competition regime) will vary according to the values of the Lagrange multipliers associated with each of these two constraints. In the homogeneous case, the set of oligopolistic equilibria will be shown to include the Cournot solution at tone extreme, when competition is extremely soft, as well as the competitive equilibrium at the other extreme, when competition is extremely tough. The set of equilibria may be characterized as supply function equilibria, with firms strategy spaces restricted to the set of non-decreasing supply functions, or, alternatively, as a selected subset of the outcomes obtained by conjectural variations of a particular type (the compensating ones). The proposed concept of oligopolistic equilibrium is also applicable to an industry supplying a group of differentiated products, the homogeneous product being the limit case corresponding to perfect substitutability.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2003010.

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Date of creation: 00 Feb 2003
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Handle: RePEc:cor:louvco:2003010

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  1. Delgado, Juan & Moreno, Diego, 2004. "Coalition-proof supply function equilibria in oligopoly," Journal of Economic Theory, Elsevier, vol. 114(2), pages 231-254, February.
  2. Grossman, Sanford J, 1981. "Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs," Econometrica, Econometric Society, vol. 49(5), pages 1149-72, September.
  3. Boone, J., 2000. "Competitive pressure: The effects on investments in product and process innovation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-84400, Tilburg University.
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  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. d'Aspremont, C & Ferreira, R Dos Santos & Gerard-Varet, L-A, 1991. "Pricing Schemes and Cournotian Equilibria," American Economic Review, American Economic Association, vol. 81(3), pages 666-73, June.
  9. Aghion, Philippe & Dewatripont, Mathias & Rey, Patrick, 1999. "Competition, Financial Discipline and Growth," CEPR Discussion Papers 2128, C.E.P.R. Discussion Papers.
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  12. 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 623-29, June.
  13. Fershtman, Chaim & Judd, Kenneth L, 1987. "Equilibrium Incentives in Oligopoly," American Economic Review, American Economic Association, vol. 77(5), pages 927-40, December.
  14. Aghion, Philippe & Harris, Christopher & Vickers, John, 1997. "Competition and growth with step-by-step innovation: An example," European Economic Review, Elsevier, vol. 41(3-5), pages 771-782, April.
  15. Jonathan Eaton & Gene M. Grossman, 1986. "Optimal Trade and Industrial Policy Under Oligopoly," NBER Working Papers 1236, National Bureau of Economic Research, Inc.
  16. Shapiro, Carl, 1989. "Theories of oligopoly behavior," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 6, pages 329-414 Elsevier.
  17. Encaoua, D. & Ulph, D., 2000. "Catching-up or Leapfrogging ? The Effects of Competition on Innovation and Growth," Papiers d'Economie Mathématique et Applications 2000.97, Université Panthéon-Sorbonne (Paris 1).
  18. Boone, Jan, 2001. "Intensity of competition and the incentive to innovate," International Journal of Industrial Organization, Elsevier, vol. 19(5), pages 705-726, April.
  19. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
  20. Hugo Sonnenschein, 1968. "The Dual of Duopoly Is Complementary Monopoly: or, Two of Cournot's Theories Are One," Journal of Political Economy, University of Chicago Press, vol. 76, pages 316.
  21. James A. Brander & Barbara J. Spencer, 1983. "Strategic Commitment with R&D: The Symmetric Case," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 225-235, Spring.
  22. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
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Citations

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Cited by:
  1. Claude d’Aspremont & Rodolphe Dos Santos Ferreira & Jacques Thépot, 2007. "Hawks and doves in segmented markets : A formal approach to competitive aggressiveness," Working Papers of LaRGE Research Center 2007-04, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg (France).
  2. D’ASPREMONT, Claude & DOS SANTOS FERREIRA, Rodolphe, 2005. "Oligopolistic competition as a common agency game," CORE Discussion Papers 2005018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Claude d’Aspremont & Rodolphe Dos Santos Ferreira, 2009. "Household behavior and individual autonomy," Working Papers of BETA 2009-17, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  4. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2011. "The empirical content of Cournot competition," Center for Economic Studies - Discussion papers ces11.11, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  5. d’ASPREMONT, Claude & DOS SANTOS FERREIRA, Rodolphe, . "Price-quantity competition with varying toughness," CORE Discussion Papers RP -2085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. D'ASPREMONT, Claude & DOS SANTOS FERREIRA, Rodolphe & GERARD-VARET, Louis-André, 2004. "Strategic R&D investment, competitive toughness and growth," CORE Discussion Papers 2004014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Rodolphe Dos Santos Ferreira & Frédéric Dufourt, 2007. "Free entry equilibria with positive profits: A unified approach to quantity and price competition games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 3(2), pages 75-94.

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