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Analysis of a Dynamical Cournot Duopoly Game with Distributed Time Delay

Author

Listed:
  • 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)

Abstract

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
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    References listed on IDEAS

    as
    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

    Keywords

    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

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