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The Stackelberg equilibrium as a consistent conjectural equilibrium

Author

Listed:
  • Ludovic A. Julien

    (LEG, Université de Bourgogne)

  • Olivier Musy

    (EconomiX, Université Paris Ouest-Nanterre La Défense)

  • Aurélien W. Saidi

    (Information & Operations Management Department, ESCP Europe)

Abstract

We consider a static game with conjectural variations where some firms make conjectures while others do not. Two propositions are proved. We first show that there exists a continuum of conjectural variations such that the conjectural equilibrium locally coincides with the Stackelberg equilibrium (Proposition 1). Second, we define the conditions under which a conjectural equilibrium is a locally consistent equilibrium (i.e. such that conjectures are fulfilled). The concept of (local) consistency is restricted to firms making conjectures. Two conditions on consistency are featured: consistency within a cohort and consistency among cohorts. The Stackelberg equilibrium fulfills only the latter condition (Proposition 2). An example is provided.

Suggested Citation

  • Ludovic A. Julien & Olivier Musy & Aurélien W. Saidi, 2011. "The Stackelberg equilibrium as a consistent conjectural equilibrium," Economics Bulletin, AccessEcon, vol. 31(1), pages 938-949.
    • Handle: RePEc:ebl:ecbull:eb-10-00656
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    References listed on IDEAS

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    1. Figuieres, Charles & Tidball, Mabel & Jean-Marie, Alain, 2004. "On the effects of conjectures in a symmetric strategic setting," Research in Economics, Elsevier, vol. 58(1), pages 75-102, March.
    2. Hanif D. Sherali & Allen L. Soyster & Frederic H. Murphy, 1983. "Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations," Operations Research, INFORMS, vol. 31(2), pages 253-276, April.
    3. van Damme, Eric & Hurkens, Sjaak, 1999. "Endogenous Stackelberg Leadership," Games and Economic Behavior, Elsevier, vol. 28(1), pages 105-129, July.
    4. Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.
    5. Martin K. Perry, 1982. "Oligopoly and Consistent Conjectural Variations," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 197-205, Spring.
    6. van Damme, Eric & Hurkens, Sjaak, 1999. "Endogenous Stackelberg Leadership," Games and Economic Behavior, Elsevier, vol. 28(1), pages 105-129, July.
    7. Bresnahan, Timothy F, 1981. "Duopoly Models with Consistent Conjectures," American Economic Review, American Economic Association, vol. 71(5), pages 934-945, December.
    8. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    9. Morton I. Kamien & Nancy L. Schwartz, 1983. "Conjectural Variations," Canadian Journal of Economics, Canadian Economics Association, vol. 16(2), pages 191-211, May.
    10. Ulph, David, 1983. "Rational conjectures in the theory of oligopoly," International Journal of Industrial Organization, Elsevier, vol. 1(2), pages 131-154, June.
    11. Friedman, James W. & Mezzetti, Claudio, 2002. "Bounded rationality, dynamic oligopoly, and conjectural variations," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 287-306, November.
    12. 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 107-122, February.
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    Cited by:

    1. Ibrahim Abada & Andreas Ehrenmann, 2016. "The prisoner’s dilemma in Cournot models: when endogenizing the level of competition leads to competitive behaviors," Cambridge Working Papers in Economics 1641, Faculty of Economics, University of Cambridge.
    2. Ludovic A. Julien & Olivier Musy, 2015. "A Review of Heinrich von Stackelberg's Book: ‘Market Structure and Equilibrium’," Australian Economic Papers, Wiley Blackwell, vol. 54(1), pages 52-60, March.

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    More about this item

    Keywords

    Consistent conjectural variations; reaction functions; Stackelberg competition;
    All these keywords.

    JEL classification:

    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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