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A note on evolutionary stability of Bertrand equilibrium

Author

Listed:
  • Burkhard Hehenkamp

    (Department of Economics, University of Dortmund, D-44221 Dortmund, Germany)

  • Wolfgang Leininger

    (Department of Economics, University of Dortmund, D-44221 Dortmund, Germany)

Abstract

It is shown that the equilibrium notion of an evolutionary stable strategy (ESS) does have predictive power for standard models of Bertrand competition. This is in contrast to a recent claim by Qin and Stuart (1997). The claim is based on the observation that the solution concept ESS behaves discontinuously when finite (discrete) action games approach an infinite (continuous) action game in the limit. Furthermore, it is argued that from a model-theoretic point of view evolutionary stability in prices (i.e. in the Bertrand model) is quite different from evolutionary stability in quantities (i.e. in the Cournot model).

Suggested Citation

  • Burkhard Hehenkamp & Wolfgang Leininger, 1999. "A note on evolutionary stability of Bertrand equilibrium," Journal of Evolutionary Economics, Springer, vol. 9(3), pages 367-371.
    • Handle: RePEc:spr:joevec:v:9:y:1999:i:3:p:367-371
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    Citations

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    Cited by:

    1. Yasuhiro Shirata, 2020. "Evolution of a Collusive Price in a Networked Market," Dynamic Games and Applications, Springer, vol. 10(2), pages 528-554, June.
    2. Fanelli, Domenico, 2010. "The Role of Socially Concerned Consumers in the Coexistence of Ethical and Standard Firms," MPRA Paper 20117, University Library of Munich, Germany.
    3. Kai A. Konrad & Florian Morath & Wieland Müller, 2014. "Taxation and Market Power," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(1), pages 173-202, February.
    4. Nagel, Kai & Shubik, Martin & Paczuski, Maya & Bak, Per, 2000. "Spatial competition and price formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 546-562.
    5. Hsiao-Chi Chen & Yunshyong Chow & Shi-Miin Liu, 2024. "Dynamics of Cournot and Bertrand Firms: Exploring Imitation and Replicator Processes," Dynamic Games and Applications, Springer, vol. 14(5), pages 1057-1092, November.
    6. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
    7. Hehenkamp, Burkhard, 2002. "Sluggish Consumers: An Evolutionary Solution to the Bertrand Paradox," Games and Economic Behavior, Elsevier, vol. 40(1), pages 44-76, July.
    8. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
    9. Xavier Vilà, 2008. "A Model-To-Model Analysis of Bertrand Competition," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-11.

    More about this item

    Keywords

    Bertrand ; Oligopoly ; Evolution ; Evolutionary stability;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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