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Complex Dynamics Analysis for a Cournot-Bertrand Mixed Game Model with Delayed Bounded Rationality

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  • Junhai Ma
  • Hongwu Wang

Abstract

A Cournot-Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot-Bertrand mixed model is considered and the results show that the delayed system has the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability.

Suggested Citation

  • Junhai Ma & Hongwu Wang, 2013. "Complex Dynamics Analysis for a Cournot-Bertrand Mixed Game Model with Delayed Bounded Rationality," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, October.
    • Handle: RePEc:hin:jnlaaa:251702
    DOI: 10.1155/2013/251702
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    Cited by:

    1. Yu, Yu & Yu, Weisheng, 2021. "The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference," Applied Mathematics and Computation, Elsevier, vol. 395(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).

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