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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.

Suggested Citation

  • 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).
  • Handle: RePEc:cor:louvco:2003010
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    References listed on IDEAS

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    1. repec:eee:reecon:v:71:y:2017:i:4:p:645-649 is not listed on IDEAS
    2. Sandomirskaia, Marina, 2017. "Nash-2 equilibrium: selective farsightedness under uncertain response," MPRA Paper 83152, University Library of Munich, Germany.
    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. 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.
    5. 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.
    6. Claude d'Aspremont & Rodolphe Dos Santos Ferreira & Louis-André Gérard-Varet, 2010. "Strategic R&D investment, competitive toughness and growth," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(3), pages 273-295.
    7. repec:eee:reecon:v:71:y:2017:i:4:p:729-739 is not listed on IDEAS
    8. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2013. "The empirical content of Cournot competition," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1552-1581.
    9. d'Aspremont, Claude & Dos Santos Ferreira, Rodolphe, 2010. "Oligopolistic competition as a common agency game," Games and Economic Behavior, Elsevier, vol. 70(1), pages 21-33, September.
    10. d’Aspremont, Claude & Dos Santos Ferreira, Rodolphe, 2017. "The Dixit–Stiglitz economy with a ‘small group’ of firms: A simple and robust equilibrium markup formula," Research in Economics, Elsevier, vol. 71(4), pages 729-739.
    11. Claude d’Aspremont & Rodolphe Dos Santos Ferreira, 2016. "Oligopolistic vs. monopolistic competition: Do intersectoral effects matter?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 299-324, June.
    12. d'Aspremont, Claude & Dos Santos Ferreira, Rodolphe, 2009. "Price-quantity competition with varying toughness," Games and Economic Behavior, Elsevier, vol. 65(1), pages 62-82, January.

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