Study On The Complex Dynamic Behavior Of Mixed Duopoly Dynamic Model Under Incomplete Information

This paper studies several mixed duopoly dynamic models with incomplete information,which assumes that firms have limited rationality in competition or take into account the effects of random demand.In the course of the research,the effects of changes in parameters such as speed of adjustment,controlling stake of state-owned enterprise,and random demand on system dynamics were analyzed.The main research contents and results of this article are as follows:1.In the study of the dynamic behavior of the Cournot mixed duopoly model considering government revenue,the theoretical analysis shows that the stability of the Nash equilibrium point of the model will be affected by the government's controlling right in public-private joint enterprise.Later,during the numerical simulation of the model,a special fractal structure similar to the "eye of chaos",which is a semi-closed ring composed of forward and reverse bifurcation sequences,is found.At the same time,it was found that changes in the government's share of public-private partnerships would affect the multi-stable of the system,such as changes in the type and structure of coexisting attractors.Based on the irreversible of the built model,the topological structure of the attraction basin was studied with the help of the critical line.According to the profit curve,it is found that companies may benefit from chaos.2.In the dynamic behavior analysis of the mixed duopoly model with stochastic inverse demand function,it is found that the built model can only pass from the Nash equilibrium state to chaos through the flip bifurcation,and the enterprise can more easily reach the equilibrium state with a smaller adjustment speed.In addition,it is found that when the other parameters of the system are unchanged,the change of the adjustment speed value does not change the overall structure of the suction basin under the set of parameters.When the system parameters change,the multi-stable phenomenon may still appear,but at this time,the structure of the coexisting attractor and the shape of the attractor domain where the attractor is located will change dramatically as the parameters change.3.In the dynamic behavior analysis of the mixed duopoly model considering social welfare under random demand,the impact of changes in the value of the random demand and the speed of adjustment of the enterprise on the dynamic behavior of the model was mainly discussed.It is found that different random demand have different effects on the model's stability region,and it mainly affects the range of speed of adjustment that companies can choose during competition.In the process of numerical simulation,a complex evolutionary analysis of the model was made based on the speed of adjustment factor and the random demand factor,and it was found that the model had initial value sensitivity and multi-stable state,and the change of the random demand value would affect these two characteristics of the model,so it determines the necessity of considering random demand when making decisions.