Research Of Dynamic Evolution Of The Oligopoly Game From The Perspective Of Social Responsibility

In the view of social responsibility,a dynamic duopoly Cournot game model is established based on nonlinear inverse demand function and bounded rationality,and the global dynamic behaviors,multi-stability and synchronization of the system are studied.By introducing the dynamic adjustment mechanism,the game problem of duopoly dynamic competition is transformed into a nonlinear discrete dynamic system.The stability of the equilibrium point of the system and the complex dynamic behavior of the system after the instability of the equilibrium point are studied.The main research contents and results are as follows:1.Based on bounded rationality and nonlinear inverse demand function,the output competition model in the perspective of social responsibility is established,and the stability and bifurcation behavior of the equilibrium points are analyzed by using the stability theory.The influence of various parameters of the system on the stability of the equilibrium point is discussed.The global dynamic behavior of the system is analyzed by using the critical line and two-dimensional irreversible map.It is found that two different kinds of contact bifurcations can occur in the system,leading to the appearance of two main holes with diagonal symmetry in the attracting domain and the disappearance of chaotic attractor.By using topological conjugate map x(t+1)=?x(t)(1-(x(t))^1/2),it is proved that the one-dimensional invariant manifold of system is located on its diagonal.There is an on-off intermittently,and the decisions of two enterprises will be consistent.2.Based on the nonlinear inverse demand function,a mixed duopoly dynamic model of competition between public enterprises and private enterprises is established.It is assumed that the public enterprises in the market perform the corresponding social responsibilities,while the private enterprises employ managers,and the managers take their own profits as the pursuit goal.The stability of the boundary equilibrium points is analyzed,and the stability region of Nash equilibrium point is given.It is found that the system can lead to chaos through flip bifurcation and Neimark-Sacker bifurcation by using numerical analysis tools such as two parameter bifurcation diagram and maximum Lyapunov exponent diagram.The global dynamic behavior of the system is analyzed by using attractor and basin of attraction.Through the single parameter bifurcation diagram and the profit curve of enterprises,it is found that when the system is in a stable state,the profit of public enterprises is higher than that of private enterprises.When the system begins to bifurcate,the profit of public enterprises gradually decreases,but the profit of private enterprises gradually increases and exceeds that of public enterprises.Because the chaotic state means that the market is in a chaotic state,which is not conducive to the development of enterprises,but also damages the healthy and orderly operation of the market.So this paper attempts to use two chaos control methods to control the chaotic state of the system.3.Assuming that the publicly-owned enterprises still fulfill the corresponding corporate social responsibility,but the private owned enterprises only pursue their own profit maximization,and considering that the two enterprises produce differentiated products,a mixed duopoly dynamic game model about output competition is established.The stability and types of the equilibrium points are analyzed by using the stability theory,and the stability region of the Nash equilibrium point in the parameter space is given.Through the two parameter bifurcation diagram,it is found that the fractal structure of the closed ring "chaotic eye" and "anti chaotic eye" generated by the reverse and forward period multiplication sequence appears.The complex fractal structure is studied by using the single parameter bifurcation diagram,the maximum Lyapunov exponent diagram.The evolution of the basin of attraction at the boundary equilibrium points of the system is studied by using the basin of attraction.It is found that with the increase of the adjustment speed of private enterprises,the system will have a global bifurcation,which makes the decision-making of enterprises lose predictability.4.This paper studies the dynamic competition of two enterprises producing homogeneous products with agents at the same time,and introduces the piecewise objective function which is more compound to the actual situation,and establishes the piecewise smooth dynamic model of duopoly output competition.The existence and stability of each equilibrium points of the system are discussed.Numerical simulation shows that the system can not only have conventional bifurcations such as flip bifurcation and Neimark Sarker bifurcation,but also have unconventional bifurcations such as period-adding bifurcation and superimposed periodic bifurcation.