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

摘要

A Cournot-Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point areinvestigated. Complex dynamic properties such as bifurcation and route tochaos are analyzed using parameter basin plots. The strange attractors arealso studied when the system is in chaotic states. Furthermore, consideringthe memory of the market, a delayed Cournot-Bertrand mixed modelis considered and the results show that the delayed system has the sameNash equilibrium and has a higher chance of reaching steady states or cyclesthan the model without delay. So making full use of the historical data canimprove the system’s stability.