IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1615-d415640.html
   My bibliography  Save this article

Delay Stability of n -Firm Cournot Oligopolies

Author

Listed:
  • Akio Matsumoto

    (Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo 192-0393, Japan)

  • Ferenc Szidarovszky

    (Department of Mathematics, Corvinus University, Fövám tér 8, 1093 Budapest, Hungary)

Abstract

The dynamic behavior of n -firm oligopolies is examined without product differentiation and with linear price and cost functions. Continuous time scales are assumed with best response dynamics, in which case the equilibrium is asymptotically stable without delays. The firms are assumed to face both implementation and information delays. If the delays are equal, then the model is a single delay case, and the equilibrium is oscillatory stable if the delay is small, at the threshold stability is lost by Hopf bifurcation with cyclic behavior, and for larger delays, the trajectories show expanding cycles. In the case of the non-equal delays, the stability switching curves are constructed and the directions of stability switches are determined. In the case of growth rate dynamics, the local behavior of the trajectories is similar to that of the best response dynamics. Simulation studies verify and illustrate the theoretical findings.

Suggested Citation

  • Akio Matsumoto & Ferenc Szidarovszky, 2020. "Delay Stability of n -Firm Cournot Oligopolies," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1615-:d:415640
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1615/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1615/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    2. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    3. Tönu Puu, 2006. "Rational expectations and the Cournot-Theocharis problem," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-11, August.
    4. Akio Matsumoto & Ferenc Szidarovszky, 2018. "Dynamic Oligopolies with Time Delays," Springer Books, Springer, number 978-981-13-1786-6, December.
    5. Lampart, Marek, 2012. "Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1081-1085.
    6. M. McManus & Richard E. Quandt, 1961. "Comments on the Stability of the Cournot Oligipoly Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 136-139.
    Full references (including those not matched with items on IDEAS)

    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. Wang, Chun & Pi, Jinxiu & Zhou, Die & Tang, Wei & Yang, Guanghui, 2023. "Dynamics of n-person Cournot games with asymmetric information and heterogeneous expectations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    2. Nikolaos Chrysanthopoulos & George P. Papavassilopoulos, 2021. "Adaptive rules for discrete-time Cournot games of high competition level markets," Operational Research, Springer, vol. 21(4), pages 2879-2906, December.
    3. Fabio Lamantia & Anghel Negriu & Jan Tuinstra, 2018. "Technology choice in an evolutionary oligopoly game," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 335-356, November.
    4. Daan Lindeman & Marius I. Ochea, 2018. "Imitation Dynamics in Oligopoly Games with Heterogeneous Players," THEMA Working Papers 2018-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    6. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.
    7. Davide Radi & Laura Gardini, 2023. "Ambiguity aversion as a route to randomness in a duopoly game," Papers 2311.11366, arXiv.org.
    8. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    9. Anufriev, Mikhail & Kopányi, Dávid, 2018. "Oligopoly game: Price makers meet price takers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 84-103.
    10. Danca, Marius-F. & Lampart, Marek, 2021. "Hidden and self-excited attractors in a heterogeneous Cournot oligopoly model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Kopel, Michael & Lamantia, Fabio, 2018. "The persistence of social strategies under increasing competitive pressure," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 71-83.
    12. Lamantia, F. & Negriu, A. & Tuinstra, J., 2016. "Evolutionary Cournot competition with endogenous technology choice: (in)stability and optimal policy," CeNDEF Working Papers 16-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    13. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    14. Daan Lindeman & Marius I. Ochea, 2024. "Imitation Dynamics in Oligopoly Games with Heterogeneous Players," Games, MDPI, vol. 15(2), pages 1-26, February.
    15. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    16. Bervoets, Sebastian & Faure, Mathieu, 2020. "Convergence in games with continua of equilibria," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 25-30.
    17. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 2000. "Does information about competitors' actions increase or decrease competition in experimental oligopoly markets?," International Journal of Industrial Organization, Elsevier, vol. 18(1), pages 39-57, January.
    18. Giovanni Paolo Crespi & Davide Radi & Matteo Rocca, 2017. "Robust games: theory and application to a Cournot duopoly model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 177-198, November.
    19. Bigoni, Maria & Fort, Margherita, 2013. "Information and learning in oligopoly: An experiment," Games and Economic Behavior, Elsevier, vol. 81(C), pages 192-214.
    20. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.

    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:gam:jmathe:v:8:y:2020:i:9:p:1615-:d:415640. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.