Dynamical Study of Competition Cournot-like Duopoly Games Incorporating Fractional Order Derivatives and Seasonal Influences

Abstract

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.