Nonlinear Evolution Of Quantum Cournot Game Models With Different Cost Functions

Since the oligopoly model was pioneered by Cournot in 1838,the theory of Cournot model has been one of the hot fields in the forefront of the study of economic management.The optimal stability of its equilibrium solution is the core problem of the study.The advent of quantum game theory and nonlinear dynamic theory opens the door for solving this problem.As we know,within the framework of this theoretical basic research,there are many factors affecting the stability of the Cournot equilibrium solution,among which the form of agency cost is one of the most important factors.Different forms of expression have different impacts on the stability of the Cournot equilibrium solution.Based on this,this paper uses the organic combination of quantum game theory and nonlinear dynamic theory to study the nonlinear evolution mechanism of quantum Cournot model under different agency cost conditions,in order to provide valuable theoretical reference for oligopoly to adopt effective production strategy in the actual competitive market.The main contents of this paper are as follows:(1)Aiming at the dynamic evolution of equilibrium solution of the Cournot oligopoly model,a quantum nonlinear dynamic evolutionary game model with finite rational expectations under the condition of linear cost function is constructed.The influence of quantum entanglement and product difference on the dynamic stability of Nash equilibrium solution and its complex mechanism is studied.The stability conditions of quantum equilibrium point are determined by numerical simulation.The results show that the stability of the system can be significantly affected by the rate of product yield adjustment and the quantum entanglement when the products are different.Therefore,the introduction of quantum entanglement can significantly reduce the stability of the system.By adjusting the quantum entanglement,we can effectively control the chaotic state of the system.Finally,the reliability of the results is verified by numerical simulation from the singular attractor and initial condition sensitivity.(2)In view of the many factors affecting the dynamic evolution of equilibrium solution of the Cournot oligopoly model,the linear cost function is replaced by nonlinear cost function,and the quantum Cournot dynamic model under the condition of adaptability expectation is constructed.The influence of product difference degree and quantum entanglement degree on the stability of Nash equilibrium solution and the complex mechanism of the system is analyzed.The results show that the system will appear bifurcation and chaos faster due to the addition of quantum entanglement,which indicates that quantum entanglement can effectively control the chaotic phenomenon in the system.By studying the sensitivity dependence of the initial conditions in the dynamic evolution of the system,it is found that the quantum entanglement can reduce the sensitivity dependence of the initial conditions.