Complexity Analysis Of Heterogeneous Duopoly Dynamic Competition Based On Consumer Surplus

Based on the consumer surplus(CS)in corporate social responsibility(CSR),this paper considers two enterprises that produce homogeneous products and compete with each other based on output,respectively adopt different expectation rules to establish nonlinear duopoly dynamic game model,and studies the dynamic evolution law of the model.Through numerical simulation,the influences of the adjustment speed of enterprises,consumer surplus parameters,maximum market price,marginal cost and other parameters on the system stability are analyzed.Complex dynamical behaviors in systems such as attractors and multisteadiness are discussed.The main content of this paper are as follows:1.Firm 1 adopts bounded rational expectation and firm 2 adopts adaptive expectation to establish dynamic game model of duopoly.The existence and stability conditions of boundary equilibrium points and Nash equilibrium points of the model are discussed.The influence of parameters on the stability of the system is studied by using single parameter bifurcation diagram and maximum Lyapunov exponent diagram,and the stability domain is drawn.The system changes from a stable state to a chaotic state through flip bifurcation.By means of irreversible mapping knowledge and critical boundary,the topological structure of the suction basin is analyzed.It is found that the critical boundary divides the phase space into two parts with different first-order preimages.The attractor coexistence phenomenon is studied when the initial values are different.The global bifurcation occurs when the attractor touches the boundary of the corresponding basin.2.The bounded rational expectation is adopted by firm 1,and the naive expectation is adopted by firm 2 to establish a dynamic game model,in which the marginal cost and consumer surplus parameters of two firms are different.The existence and local stability conditions of equilibrium point are analyzed.The stability domain of equilibrium point is analyzed by numerical simulation,and two paths leading to chaos are studied: flip bifurcation and Neimark-Sacker bifurcation.The dynamic behavior of the system is analyzed when the marginal cost and consumer residual parameters of the two firms change.When the adjustment speed of the firms increases,the system enters the chaotic state through flip bifurcation.Through the evolution process of the attractor and the attractor basin,two groups of attractors coexist in the system.The average profit of two enterprises under different unit cost and adjustment speed is analyzed.Compared with the adjustment process of enterprises,the average profit of enterprises has a certain delay.3.The dynamic game model of Cournot duopoly under nonlinear demand function is established by taking the bounded rational expectation of firm 1 and the local approximate monopoly adjustment mechanism of firm 2.By using the eigenvalues of Jacobian matrix and Jury criterion,the types and stability conditions of equilibrium points are analyzed.The stable region of equilibrium point is described by stability region and stability curve,and the influence of marginal cost and adjustment speed on market stability is studied by using one-dimensional bifurcation diagram.The co-existence phenomenon of attractors is obtained at the "jump" point in the bifurcation diagram,and the multistability of the system is studied by observing the evolution process of basin of attraction by changing parameters.When the equilibrium point is valued in the basin of attraction.After many iterations,it finally converges to the attractor.The path into chaos when consumer surplus parameters change is analyzed by using two dimensional bifurcation diagram and phase diagram.