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Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product

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  • Wei Zhou
  • Na Zhao
  • Tong Chu
  • Ying-Xiang Chang

Abstract

In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance.

Suggested Citation

  • Wei Zhou & Na Zhao & Tong Chu & Ying-Xiang Chang, 2020. "Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product," Complexity, Hindawi, vol. 2020, pages 1-16, August.
    • Handle: RePEc:hin:complx:4580415
    DOI: 10.1155/2020/4580415
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    Cited by:

    1. Chu, Tong & Zhou, Wei, 2022. "Complex dynamics of R&D competition with one-way spillover based on intellectual property protection," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Liu, Yuxia & Zhou, Wei & Wang, Qian, 2022. "Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Liu, Cui & He, Rui-chun & Zhou, Wei & Li, Hui, 2021. "Dynamic analysis of airline bidding game based on nonlinear cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    4. Zhu, Yan-lan & Zhou, Wei & Chu, Tong, 2022. "Analysis of complex dynamical behavior in a mixed duopoly model with heterogeneous goods," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    5. Li, Hui & Zhou, Wei & Elsadany, A. A & Chu, Tong, 2021. "Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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