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Nonlinear analysis and chaos control of the complex dynamics of multi-market Cournot game with bounded rationality

Author

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  • Zhao, LiuWei
  • Du, Jianguo
  • Wang, QiWei

Abstract

In this work, a dynamic multi-market Cournot model is introduced based on a multi-markets’ specific inverse demand function. Puu’s incomplete information approach, as a realistic method, is used to contract the corresponding dynamical model under this function. Therefore, some stability analysis is used by the model to detect the stability and instability conditions of the system’s Nash equilibrium. Based on the analysis, some dynamic phenomena such as bifurcation and chaos are found. Numerical simulations and the Maximum Lyapunov exponent are used to provide experimental evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium points of the system can loose stability via flip bifurcation or Neimark–Sacher bifurcation and time-delayed feedback control is used to stabilize the chaotic behaviors of the system.

Suggested Citation

  • Zhao, LiuWei & Du, Jianguo & Wang, QiWei, 2019. "Nonlinear analysis and chaos control of the complex dynamics of multi-market Cournot game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 45-57.
    • Handle: RePEc:eee:matcom:v:162:y:2019:i:c:p:45-57
    DOI: 10.1016/j.matcom.2019.01.004
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    References listed on IDEAS

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    1. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    2. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    3. Pascal Billand & Christophe Bravard & Subhadip Chakrabarti & Sudipta Sarangi, 2014. "A note on networks of collaboration in multi-market oligopolies," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(2), pages 325-335, September.
    4. LiuWei Zhao, 2016. "Analysis and Control of the Complex Dynamics of a Multimarket Cournot Investment Game with Bounded Rationality," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-10, May.
    5. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    6. 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.
    7. Spence, Michael, 1976. "Product Differentiation and Welfare," American Economic Review, American Economic Association, vol. 66(2), pages 407-414, May.
    8. 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.
    9. LiuWei Zhao, 2017. "Nonlinear Complex Dynamics of Carbon Emission Reduction Cournot Game with Bounded Rationality," Complexity, Hindawi, vol. 2017, pages 1-10, October.
    10. Pascal Billand & Christophe Bravard & Subhadip Chakrabarti & Sudipta Sarangi, 2014. "A Note on Networks of Collaboration in Multi-market Oligopolies," Post-Print halshs-00878943, HAL.
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    Cited by:

    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. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    3. Zhao, Liuwei & Jin, Shuai & Jiang, Hongyun, 2022. "Investigation of complex dynamics and chaos control of the duopoly supply chain under the mixed carbon policy," Chaos, Solitons & Fractals, Elsevier, vol. 164(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).

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