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Do Followers Really Matter in Stackelberg Competition?

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  • Ludovic Julien
  • Olivier Musy
  • Aurélien Saïdi

Abstract

In this paper, we consider a T-stage linear model of Stackelberg oligopoly. First, we show geometrically and analytically that under the two conditions of linear market demand and identical constant marginal costs, the T-stage Stackelberg model reduces to a model where T oligopolies exploit residual demand sequentially. At any stage, leaders behave as if followers did not matter. Second, we study social welfare and convergence toward competitive equilibrium. Especially, we consider the velocity of convergence as the number of firms increases. The convergence is faster when reallocating firms from the most to the less populated cohort until equalizing the size of all cohorts.

Suggested Citation

  • Ludovic Julien & Olivier Musy & Aurélien Saïdi, 2011. "Do Followers Really Matter in Stackelberg Competition?," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 75, pages 11-27.
  • Handle: RePEc:lde:journl:y:2011:i:75:p:11-27
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    References listed on IDEAS

    as
    1. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    2. Ludovic Julien & Olivier Musy & Aurélien Saïdi, 2012. "On hierarchical competition in oligopoly," Journal of Economics, Springer, vol. 107(3), pages 217-237, November.
    3. Anderson, Simon P. & Engers, Maxim, 1992. "Stackelberg versus Cournot oligopoly equilibrium," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 127-135, March.
    4. Federico Etro, 2008. "Stackelberg Competition with Endogenous Entry," Economic Journal, Royal Economic Society, vol. 118(532), pages 1670-1697, October.
    5. Boyer, Marcel & Moreaux, Michel, 1986. "Perfect competition as the limit of a hierarchical market game," Economics Letters, Elsevier, vol. 22(2-3), pages 115-118.
    6. Daughety, Andrew F, 1990. "Beneficial Concentration," American Economic Review, American Economic Association, vol. 80(5), pages 1231-1237, December.
    7. Ludovic A. Julien & Olivier Musy, 2011. "A Generalized Oligopoly Model With Conjectural Variations," Metroeconomica, Wiley Blackwell, vol. 62(3), pages 411-433, July.
    8. John S. Heywood & Matthew McGinty, 2007. "Mergers among leaders and mergers among followers," Economics Bulletin, AccessEcon, vol. 12(12), pages 1-7.
    9. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
    10. John S. Heywood & Matthew McGinty, 2008. "Leading and Merging: Convex Costs, Stackelberg, and the Merger Paradox," Southern Economic Journal, Southern Economic Association, vol. 74(3), pages 879-893, January.
    11. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, January.
    12. Richard Watt, 2002. "A Generalized Oligopoly Model," Metroeconomica, Wiley Blackwell, vol. 53(1), pages 46-55, February.
    13. Pal, Debashis & Sarkar, Jyotirmoy, 2001. "A Stackelberg Oligopoly with Nonidentical Firms," Bulletin of Economic Research, Wiley Blackwell, vol. 53(2), pages 127-134, April.
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    More about this item

    Keywords

    leader's markup discount ratio; linear economy; follower's output index; generalized Stackelberg competition;

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L20 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - General

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