Dynamic Evolution Analysis Of Oligopoly Game Model Under Isoelastic Demand

As the competition among enterprises becomes more and more intense,linear demand has been unable to adapt to the complex and changeable form of the actual market,so we need to consider the inverse demand function which is more in line with the actual market competition environment.The isoelastic demand function is a typical nonlinear demand function,and it ensures the uniqueness of the existence of Nash equilibrium.Therefore,this paper studies the dynamic evolution process of oligopoly game model based on isoelastic demand.On the basis of isoelastic demand,the local and global dynamic behaviors of oligopoly games with strategic delegation,nonlinear cost and consumer surplus are analyzed,respectively.The main contents of this paper are as follows:First of all,a dynamic Cournot duopoly game model based on isoelastic demand and strategic delegation is established.The local stability of the system at each equilibrium point is analyzed using the eigenvalues and Jury criterion,and the corresponding stability conditions are derived.And how each parameter affects the stability of the system is analyzed,and it is found that when enterprise managers choose smaller the speed of adjustment,relatively larger price elasticity,relatively small profit weight coefficient and relatively small marginal cost,it is more conducive to the development of enterprises.In addition,the coexistence of attractors is studied through the basin of attraction,and it is found that the jumping phenomenon in the one-dimensional bifurcation diagram is due to the coexistence of attractors.Finally,the topological structure of the basin of attraction and the global dynamics of the system are analyzed by using the basin of attraction,the critical curve and the noninvertible map.It is found that when the critical curve is in contact with the boundary of the basin of attraction,and when the attractor is in contact with the boundary of the basin of attraction,the global dynamic behavior of the system occurs.Secondly,on the basis of the previous model,a dynamic oligopoly game model with nonlinear cost and strategic delegation is established,and the stable region of the Nash equilibrium point is obtained through the Jury criterion,and the system may pass through Flip bifurcation and Neimark-Sacker bifurcation loses its stability.The influence of various parameters on the stability of the system and the coexistence of attractors are analyzed by 1-D bifurcation diagram,the largest Lyapunov exponent diagram and the basin of attraction.In addition,with the help of the critical curve and the basin of attraction,the global bifurcation phenomenon caused by the generation and disappearance of the "hole" in the basin of attraction is analyzed,and the boundary of the chaotic attractor is given by using the critical curve,and the region with higher density of points is also given,that is,the region where the points of the general trajectory in the invariant region are visited more frequently.Finally,on the basis of the first model,a dynamic duopoly game model with consumer surplus is established,and it is concluded that the model has three equilibrium points.The local stability of the boundary equilibrium point is studied by using stability theory and Jacobian matrix,and the stability condition of Nash equilibrium point is obtained by Jury criterion.The single-parameter bifurcation diagram,the two-dimensional bifurcation diagram and profit curve are drawn by numerical simulation,and how each parameter affects the stability of the system is analyzed,and the complex dynamic behavior of the system is analyzed with the help of basin of attraction,the absorbing area and the critical curve.It is found that when the speed of adjustment,profit weight coefficient and marginal cost selected by the enterprise are relatively small,and the price elasticity coefficient is relatively large,the enterprise development will be more stable.