Research On The Complexity Of The Nash Equilibrium Strategy Of The Cournot Game Model Based On Quantum Game Theory

Quantum game theory is an interdisciplinary study of game theory with quantum information theory as a tool.Due to the introduction of quantum entanglement,the strategy space of participants can be expanded,which can solve some problems that can not be solved by classical games.Therefore,it is widely used in economics,information science and other fields.The problem of Nash equilibrium strategy has always been a core problem in the oligopoly market and has been widely concerned.There are basically two approaches to research around this problem.The first is to use nonlinear dynamics theory to study the dynamic complexity of Nash equilibrium and the complex dynamics that appear in the unsteady state.The second is to use quantum game theory to explore the Pareto optimal realization of oligopoly equilibrium.Combining quantum game theory with nonlinear dynamic theory,and then analyzing the dynamic complexity of oligopoly model under bounded rationality behavior,few scholars have done this kind of discussion at present.Based on this,this paper uses quantum game theory and nonlinear dynamics theory to construct a quantum Cournot nonlinear dynamic model with different rational expectations under different participant conditions,and analyzes the impact of quantum entanglement,the speed of firm output adjustment and other related factors.The stability of the Nash equilibrium and the influence of the complex dynamic behavior of the system are further explored to explore the characteristics of the dynamic complexity of the model,which can provide references for the selection strategies of competing firms in reality.The main contents are as follows:(1)Aiming at the complexity of the Nash equilibrium of the Cournot duopoly model,using quantum game theory and nonlinear dynamic systems,constructing a duopoly quantum Cournot nonlinear dynamic model with different expectations.We analyze the effect of quantum entanglement degree on stability of the equilibrium points and complex dynamics behaviors.The results show that quantum entanglement degree can enhance the stability of the system.When the adjustment speed of the two firms output reaches a certain level,it will lead to complex chaotic characteristics of the system,and the entanglement degree can effectively can control the system's chaos.Finally,numerical simulations demonstrate the correction of the theory via bifurcation and sensitivity to initial conditions.(2)Then expand on the basis of the quantum Cournot nonlinear dynamic model,introduce firm with naive expectation,construct a three-oligarch quantum Cournot nonlinear dynamic model.We analyze the effect of quantum entanglement degree on stability of the equilibrium points and complex dynamics behaviors.The results show that with the increase in the speed of firm output adjustment,the system will be bifurcated and chaotic.Increasing the degree of entanglement can reduce the sensitive dependence of the initial conditions in the dynamic evolution of the system,and can effectively control the chaotic state of the system.In addition,compared with the duopoly quantum Cournot nonlinear dynamic model,increasing participants will make the system appear bifurcation and chaos faster.