Global Dynamics of an Oligopoly Competition Model with Isoelastic Demand and Strategic Delegation

In this paper, we research a dynamic Cournot duopoly game model based on isoelastic demand and strategic delegation. The local stability and stability conditions of each equilibrium point of the system are discussed by eigenvalues and Jury criterion. We also discuss the influence of parameters on system stability, and we find that when enterprise managers choose smaller the speed of adjustment, relatively large price elasticity, relatively small profit weight coefficient and relatively small marginal cost, the enterprises will have better development, and the enterprise managers will get more reward. Then the problem of attractor coexistence is studied through the basin of attraction, and it is found that the jump phenomenon in the one-dimensional bifurcation diagram is due to attractors coexistence. 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, the attractor and the boundary of the basin of attraction, global dynamic behaviors occur in the system