IDEAS home Printed from
   My bibliography  Save this article

Analysis of a Dynamical Cournot Duopoly Game with Distributed Time Delay


  • Nicoleta SÎRGHI

    (Faculty of Economics and Business Administration, West University of Timisoara, Romania)

  • Mihaela NEAMŢU

    (Faculty of Economics and Business Administration, West University of Timisoara, Romania)

  • Petru Claudiu STRĂIN

    (Faculty of Mathematics and Informatics, West University of Timisoara, Romania)


The aim of the paper is to analyze the dynamic model of the Cournot duopoly game with bounded rationality associated to two firms. We consider the cost function of the first firm as nonlinear and for the second firm as linear. The players do not have a complete knowledge of the market and they follow a bounded rationality adjustment process based on the estimation of the marginal profit. Also, the distributed time delay is introduced, because the decisions at the current time depend on the average past decisions. The mathematical model is described by a distributed delay differential system with two nonlinear equations. The study for the local stability of the Nash equilibrium point is carried out in the case of two types of kernels: weak (exponential) and Dirac. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. The delays are considered as bifurcation parameters. In some conditions of the parameters of the model, we have proved that a family of periodic solutions bifurcates from the equilibrium point when the bifurcation parameter passes through a critical value. Numerical simulations are performed to illustrate the effectiveness of our results. Finally, conclusions and future researches are provided.

Suggested Citation

  • Nicoleta SÎRGHI & Mihaela NEAMŢU & Petru Claudiu STRĂIN, 2015. "Analysis of a Dynamical Cournot Duopoly Game with Distributed Time Delay," Timisoara Journal of Economics and Business, West University of Timisoara, Romania, Faculty of Economics and Business Administration, vol. 8(1s), pages 1-13, February.
  • Handle: RePEc:wun:timjeb:tjeb:v08:y2015:i01s:a01

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
    2. Agiza, H.N. & Hegazi, A.S. & Elsadany, A.A., 2002. "Complex dynamics and synchronization of a duopoly game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 133-146.
    3. Onozaki, Tamotsu & Sieg, Gernot & Yokoo, Masanori, 2003. "Stability, chaos and multiple attractors: a single agent makes a difference," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1917-1938, August.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Cournot duopoly game; Cournot Model; Bounded Rationality; distributed time delay; local stability; Hopf bifurcation.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations


    Access and download statistics


    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:wun:timjeb:tjeb:v08:y2015:i01s:a01. 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: (Romeo Margea). General contact details of provider: .

    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.