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

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

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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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. d'ASPREMONT, Claude & DOS SANTOS FERREIRA, Rodolphe & GERARD-VARET, Louis-André, . "Pricing schemes and Cournotian equilibria," CORE Discussion Papers RP -943, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. 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.
  3. 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.
  4. Boone, Jan, 2001. "Intensity of competition and the incentive to innovate," International Journal of Industrial Organization, Elsevier, vol. 19(5), pages 705-726, April.
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  6. Charles A. Holt & David T. Scheffman, 1987. "Facilitating Practices: The Effects of Advance Notice and Best-Price Policies," RAND Journal of Economics, The RAND Corporation, vol. 18(2), pages 187-197, Summer.
  7. Vickers, John, 1985. "Delegation and the Theory of the Firm," Economic Journal, Royal Economic Society, vol. 95(380a), pages 138-47, Supplemen.
  8. 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.
  9. Jonathan Eaton & Gene M. Grossman, 1983. "Optimal Trade and Industrial Policy Under Oligopoly," NBER Working Papers 1236, National Bureau of Economic Research, Inc.
  10. Grossman, Gene M & Helpman, Elhanan, 1991. "Quality Ladders and Product Cycles," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 557-86, May.
  11. 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.
  12. Aghion, Philippe & Dewatripont, Mathias & Rey, Patrick, 1999. "Competition, Financial Discipline and Growth," Scholarly Articles 12490416, Harvard University Department of Economics.
  13. 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.
  14. 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).
  15. Jan Boone, 2000. "Competitive Pressure: The Effects on Investments in Product and Process Innovation," RAND Journal of Economics, The RAND Corporation, vol. 31(3), pages 549-569, Autumn.
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  18. repec:ner:tilbur:urn:nbn:nl:ui:12-84400 is not listed on IDEAS
  19. Delgado, Juan & Moreno, Diego, 2004. "Coalition-proof supply function equilibria in oligopoly," Journal of Economic Theory, Elsevier, vol. 114(2), pages 231-254, February.
  20. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
  21. 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.
  22. Harris, Christopher & Howitt, Peter & Vickers, John & Aghion, Philippe, 2001. "Competition, Imitation and Growth with Step-by-Step Innovation," Scholarly Articles 12375013, Harvard University Department of Economics.
  23. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-22, February.
  24. Fershtman, Chaim & Judd, Kenneth L, 1987. "Equilibrium Incentives in Oligopoly," American Economic Review, American Economic Association, vol. 77(5), pages 927-40, December.
  25. 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.
  26. van de Klundert, Theo & Smulders, Sjak, 1997. " Growth, Competition and Welfare," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 99-118, March.
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