Complexity Analysis About Nonlinear Mixed Oligopolies Game Based on Production Cooperation

Under the influence of "the Belt and Road Initiative" launched by Chinese Government, many Chinese oligopoly enterprises begin to select certain international partners and transfer some low-end production to overseas, while keeping some of the high-end links domestic. Therefore, these enterprises form competition at both sides. To represent such a competitive status, we establish a four-oligopoly mixed game model of upstream and downstream, and examine the complexity of its characteristics. After identifying the importance of the parameters, we consider the stable region of three dimensions and based on which find the equilibrium point. The influence of the parameters on the stability of the system is then studied. Using two parameter bifurcation diagrams, we find the largest Lyapunov exponent of the two parameters, which represents the path of the system and the complexity of the system. We also discuss the effect of the system instability on the average profit of the two sides with 3-D and 4-D average profit graphs.