IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v57y2013i3p707-718.html
   My bibliography  Save this article

On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility

Author

Listed:
  • Pierre von Mouche
  • Federico Quartieri

Abstract

We consider a class of homogeneous Cournot oligopolies with concave integrated price flexibility and convex cost functions. We provide new results about the semi-uniqueness and uniqueness of (Cournot) equilibria for the oligopolies that satisfy these conditions. The condition of concave integrated price flexibility is implied by (but does not imply) the log-concavity of a continuous decreasing price function. So, our results generalize previous results for decreasing log-concave price functions and convex cost functions. We also discuss the particular type of quasi-concavity that characterizes the conditional revenue and profit functions of the firms in these oligopolies and we point out an error of the literature on the equilibrium uniqueness in oligopolies with log-concave price functions. Finally, we explain how the condition of concave integrated price flexibility relates to other conditions on the price and aggregate revenue functions usually considered in the literature, e.g., their concavity. Copyright The Author(s) 2013

Suggested Citation

  • Pierre von Mouche & Federico Quartieri, 2013. "On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility," Journal of Global Optimization, Springer, vol. 57(3), pages 707-718, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:707-718
    DOI: 10.1007/s10898-012-9926-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9926-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9926-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Christian Ewerhart, 2009. "Cournot Oligopoly and Concavo-Concave Demand," IEW - Working Papers 427, Institute for Empirical Research in Economics - University of Zurich.
    2. Amir, R., 1996. "Cournot oligopoly and theory of supermodular games," LIDAM Reprints CORE 1228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    4. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pierre von Mouche & Federico Quartieri, 2015. "Cournot Equilibrium Uniqueness in Case of Concave Industry Revenue: a Simple Proof," Economics Bulletin, AccessEcon, vol. 35(2), pages 1299-1305.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rabah Amir & Filomena Garcia & Malgorzata Knauff, 2006. "Endogenous Heterogeneity in Strategic Models: Symmetry-breaking via Strategic Substitutes and Nonconcavities," Working Papers Department of Economics 2006/29, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    2. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    3. Antonio Tesoriere, 2015. "Competing R&D joint ventures in Cournot oligopoly with spillovers," Journal of Economics, Springer, vol. 115(3), pages 231-256, July.
    4. Xavier Vives, 2008. "Innovation And Competitive Pressure," Journal of Industrial Economics, Wiley Blackwell, vol. 56(3), pages 419-469, December.
    5. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2019. "Submodular Mean Field Games. Existence and Approximation of Solutions," Center for Mathematical Economics Working Papers 621, Center for Mathematical Economics, Bielefeld University.
    6. Amir, Rabah & Lazzati, Natalia, 2011. "Network effects, market structure and industry performance," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2389-2419.
    7. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    8. Schipper, Burkhard C, 2011. "Strategic control of myopic best reply in repeated games," MPRA Paper 30219, University Library of Munich, Germany.
    9. Lagerlof, Johan N.M., 2007. "Insisting on a non-negative price: Oligopoly, uncertainty, welfare, and multiple equilibria," International Journal of Industrial Organization, Elsevier, vol. 25(4), pages 861-875, August.
    10. Carlos Alós Ferrer & Ana B. Ania, 2002. "The Evolutionary Logic of Feeling Small," Vienna Economics Papers 0216, University of Vienna, Department of Economics.
    11. Einy, Ezra & Haimanko, Ori & Moreno, Diego & Shitovitz, Benyamin, 2010. "On the existence of Bayesian Cournot equilibrium," Games and Economic Behavior, Elsevier, vol. 68(1), pages 77-94, January.
    12. Graevenitz, Georg von, 2004. "Spillovers Reconsidered: Analysing Economic Welfare under complementarities in R&D," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 29, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    13. KNAUFF, Malgorzata, 2006. "Market transparency and Bertrand competition," LIDAM Discussion Papers CORE 2006037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Amir, Rabah, 2005. "Ordinal versus cardinal complementarity: The case of Cournot oligopoly," Games and Economic Behavior, Elsevier, vol. 53(1), pages 1-14, October.
    15. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    16. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    17. Gazi I. Kara & S. Mehmet Ozsoy, 2016. "Bank regulation under fire sale externalities," Finance and Economics Discussion Series 2016-026, Board of Governors of the Federal Reserve System (U.S.).
    18. Alexandrov, Alexei & Bedre-Defolie, Özlem, 2017. "LeChatelier–Samuelson principle in games and pass-through of shocks," Journal of Economic Theory, Elsevier, vol. 168(C), pages 44-54.
    19. Anne-Christine Barthel & Eric Hoffmann, 2020. "On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies," Theory and Decision, Springer, vol. 88(4), pages 471-491, May.
    20. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.

    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:spr:jglopt:v:57:y:2013:i:3:p:707-718. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.