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Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter

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  • Du, Jian-guo
  • Fan, Yue-qian
  • Sheng, Zhao-han
  • Hou, Yun-zhang

Abstract

In actual economies, players sometimes would offer an upper limiter to their output due to capacity constraints, financial constraints and cautious response to uncertainty in the world, or offer a lower limiter to their output due to economies of scale or break-even consideration. In this paper, we discuss a dynamic duopoly game with heterogeneous players by assuming that one of them imposes an upper limiter on output, and the other one imposes a lower limiter. We analyze how the limiter affects the dynamics of output and the performance of players, and explore the number of the equilibrium points and the distribution of conditioned equilibrium points of the model. We then discuss the stable region of conditioned equilibrium. The theoretical results and numerical experiments show that adding appropriate limiter can make the system more robust, and even get rid of its chaos. The numerical results show that chaotic output dynamics can be beneficial to one firm but harmful to the other, and can also be harmful to both of them, and also show that adding appropriate limiter can improve the performance of the player.

Suggested Citation

  • Du, Jian-guo & Fan, Yue-qian & Sheng, Zhao-han & Hou, Yun-zhang, 2013. "Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter," Economic Modelling, Elsevier, vol. 33(C), pages 507-516.
    • Handle: RePEc:eee:ecmode:v:33:y:2013:i:c:p:507-516
    DOI: 10.1016/j.econmod.2013.04.045
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    References listed on IDEAS

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    Cited by:

    1. Cavalli, Fausto & Naimzada, Ahmad, 2016. "Complex dynamics and multistability with increasing rationality in market games," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 151-161.
    2. Yu Yu & Weisheng Yu, 2019. "The Complexion of Multi-period Stackelberg Triopoly Game with Bounded Rationality," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 457-478, January.
    3. 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.
    4. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    5. Shi, Lian & Sheng, Zhaohan & Xu, Feng, 2015. "The dynamics of competition in remanufacturing: A stability analysis," Economic Modelling, Elsevier, vol. 50(C), pages 245-253.
    6. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.
    7. A. A. Elsadany & A. M. Awad, 2016. "Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 617-639, December.

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    More about this item

    Keywords

    Duopoly games; Limiter; Conditioned equilibrium; Chaos control; Performance;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance

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