Complex dynamics of Cournot-Bertrand duopoly game with peer-induced fairness and delay decision

Abstract

<p style='text-indent:20px;'>This paper establishes the Cournot-Bertrand duopoly game models with bounded rationality expectations under the assumption that the players are fair-minded agents who may adopt the delay decision. The existence and local stability of the equilibrium points are investigated. The effects of key parameters on the long-term dynamical evolution process of the models are investigated by numerical simulation. Furthermore, the performance of the players is examined using average profit and utility indexes. The results reveal that the excessively fast adjustment speeds and the higher fairness concern coefficients have a strong destabilizing impact on the system's stability. The product differentiation degree and delay strategy may be strong stabilizing or destabilizing factors for the game, which indicates that an appropriate product differentiation degree or delay weight is conducive to the system preserving its stability. In addition, when the system falls into periodic cycles or chaotic motions, the change trends of the players' performance may elevate or decline depending on the specific parameter conditions. Therefore, the chaos does not always necessarily detrimental to all the players in the Cournot-Bertrand duopoly game.</p>