IDEAS home Printed from https://ideas.repec.org/p/gre/wpaper/2017-10.html
   My bibliography  Save this paper

On the Coalitional Stability of Monopoly Power in Differentiated Bertrand and Cournot Oligopolies

Author

Listed:
  • Aymeric Lardon

    (Université Côte d'Azur, France
    GREDEG CNRS)

Abstract

In this article we revisit the classic comparison between Bertrand and Cournot competition in the presence of a cartel of firms that faces outsiders acting individually. This competition setting enables to deal with both non-cooperative and cooperative oligopoly games. We concentrate on industries consisting of symmetrically differentiated products where firms operate at a constant and identical marginal cost. First, while the standard Bertrand-Cournot rankings still hold for Nash equilibrium prices, we show that the results may be altered for Nash equilibrium quantities and profits.Second, we define cooperative Bertrand and Cournot oligopoly games with transferable utility on the basis of their non-cooperative foundation. We establish that the core of a cooperative Cournot oligopoly game is strictly included in the core of a cooperative Bertrand oligopoly game when the number of firms is lower or equal to 25. Otherwise the cores cannot be compared. Moreover, we focus on the aggregate-monotonic core, a subset of the core, that has the advantage to select point solutions satisfying both core selection and aggregate monotonicity properties. We succeed in comparing the aggregate-monotonic cores between Bertrand and Cournot competition regardless of the number of firms.

Suggested Citation

  • Aymeric Lardon, 2017. "On the Coalitional Stability of Monopoly Power in Differentiated Bertrand and Cournot Oligopolies," GREDEG Working Papers 2017-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
  • Handle: RePEc:gre:wpaper:2017-10
    as

    Download full text from publisher

    File URL: http://www.gredeg.cnrs.fr/working-papers/GREDEG-WP-2017-10.pdf
    File Function: First version, 2017
    Download Restriction: no

    References listed on IDEAS

    as
    1. Stéphane Gonzalez & Aymeric Lardon, 2018. "Optimal deterrence of cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 207-227, March.
    2. Dastidar, Krishnendu Ghosh, 1997. "Comparing Cournot and Bertrand in a Homogeneous Product Market," Journal of Economic Theory, Elsevier, vol. 75(1), pages 205-212, July.
    3. Driessen, Theo S.H. & Meinhardt, Holger I., 2005. "Convexity of oligopoly games without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 102-126, July.
    4. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    5. Zhao, Jingang, 1999. "A [beta]-Core Existence Result and Its Application to Oligopoly Markets," Games and Economic Behavior, Elsevier, vol. 27(1), pages 153-168, April.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. X. Wang & Jingang Zhao, 2010. "Why are firms sometimes unwilling to reduce costs?," Journal of Economics, Springer, vol. 101(2), pages 103-124, October.
    8. Zhao, J, 1996. "A B-Core Existence Result and its Application to Oligopoly Markets," ISER Discussion Paper 0418, Institute of Social and Economic Research, Osaka University.
    9. Okuguchi, Koji, 1987. "Equilibrium prices in the Bertrand and Cournot oligopolies," Journal of Economic Theory, Elsevier, vol. 42(1), pages 128-139, June.
    10. Stephen W. Salant & Sheldon Switzer & Robert J. Reynolds, 1983. "Losses From Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 185-199.
    11. Amir, Rabah & Jin, Jim Y., 2001. "Cournot and Bertrand equilibria compared: substitutability, complementarity and concavity," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 303-317, March.
    12. Aymeric Lardon, 2018. "Convexity of Bertrand oligopoly TU-games with differentiated products," Post-Print halshs-00544056, HAL.
    13. Pal, Rupayan, 2015. "Cournot vs. Bertrand under relative performance delegation: Implications of positive and negative network externalities," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 94-101.
    14. Leonard Cheng, 1985. "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 146-152, Spring.
    15. Norde, Henk & Pham Do, Kim Hang & Tijs, Stef, 2002. "Oligopoly games with and without transferable technologies," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 187-207, March.
    16. Paraskevas Lekeas & Giorgos Stamatopoulos, 2014. "Cooperative oligopoly games with boundedly rational firms," Annals of Operations Research, Springer, vol. 223(1), pages 255-272, December.
    17. 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.
    18. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    19. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    20. Aymeric Lardon, 2012. "The γ-core in Cournot oligopoly TU-games with capacity constraints," Theory and Decision, Springer, vol. 72(3), pages 387-411, March.
    21. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
    22. Lofaro, Andrea, 2002. "On the efficiency of Bertrand and Cournot competition under incomplete information," European Journal of Political Economy, Elsevier, vol. 18(3), pages 561-578, September.
    23. Vives, Xavier, 1985. "On the efficiency of Bertrand and Cournot equilibria with product differentation," Journal of Economic Theory, Elsevier, vol. 36(1), pages 166-175, June.
    24. Raymond Deneckere & Carl Davidson, 1985. "Incentives to Form Coalitions with Bertrand Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(4), pages 473-486, Winter.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bertrand; Cournot; Differentiated oligopoly; Cartel; Nash equilibrium; Core; Aggregate-monotonic core;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gre:wpaper:2017-10. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Patrice Bougette). General contact details of provider: http://edirc.repec.org/data/credcfr.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.