Abstract Cournot’s game is one of the most distinguished and influential economic models. However, the classical integer order derivatives utilized in Cournot’s game lack the efficiency to simulate the significant memory characteristics observed in many economic systems. This work aims at introducing a dynamical study of a more realistic proposed competition Cournot-like duopoly game having fractional order derivatives. Sufficient conditions for existence and uniqueness of the new model’s solution are obtained. The existence and local stability analysis of Nash equilibrium points along with other equilibrium points are examined. Some aspects of global stability analysis are treated. More significantly, the effects of seasonal periodic perturbations of parameters values are also explored. The multiscale fuzzy entropy measurements for complexity are employed for this case. Numerical simulations are presented in order to verify the analytical results. It is observed that the time-varying parameters induce very complicated dynamics in perturbed Cournot duopoly game compared with the unperturbed game.

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包含分数阶导数和季节性影响的类古诺双头垄断博弈的动力学研究

摘要 古诺博弈是最著名和最有影响力的经济模型之一。然而，古诺博弈中使用的经典整数阶导数缺乏模拟在许多经济系统中观察到的显着记忆特征的效率。这项工作旨在引入对具有分数阶导数的更现实的竞争类古诺双寡头博弈的动态研究。得到了新模型解存在唯一性的充分条件。检查了纳什均衡点与其他均衡点的存在性和局部稳定性分析。处理了全局稳定性分析的某些方面。更重要的是，还探讨了参数值的季节性周期性扰动的影响。在这种情况下，采用了复杂性的多尺度模糊熵测量。为了验证分析结果，给出了数值模拟。观察到，与未扰动博弈相比，时变参数在扰动古诺双头垄断博弈中引起非常复杂的动力学。