Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation

In this paper, we propose a dynamic Cournot duopoly game model based on isoelastic demand and strategic delegation. The local stability conditions of each equilibrium point of the system are discussed. We also investigate the influence of parameters on system stability, and we find that with smaller speed of adjustment, relatively large price elasticity, relatively small profit weight coefficient and marginal cost, the duopoly is more stable. Then the problem of coexistence of attractors is studied through the basin of attraction, and it is found that the jump phenomenon in the one-dimensional bifurcation diagram is due to coexistence of attractors. Finally, the structure of the basins of attraction and the global dynamics of the system are analyzed by using critical curves. It is found that when a critical curve or an attractor contact with the boundary of the basin of attraction, global bifurcations occur in the system.