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.

[1]  Jonas Häckner,et al.  A Note on Price and Quantity Competition in Differentiated Oligopolies , 2000, J. Econ. Theory.

[2]  Karl Worthmann,et al.  Model Predictive Control of Nonholonomic Mobile Robots Without Stabilizing Constraints and Costs , 2016, IEEE Transactions on Control Systems Technology.

[3]  A. Naimzada,et al.  Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products , 2012 .

[4]  Junhai Ma,et al.  Price game and chaos control among three oligarchs with different rationalities in property insurance market. , 2012, Chaos.

[5]  Junhai Ma,et al.  Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System , 2016, Int. J. Bifurc. Chaos.

[6]  Lijian Sun,et al.  Complexity analysis and chaos control of a R&D game with spillovers and endogenous demand in a triopoly , 2015 .

[7]  Junhai Ma,et al.  The research on Cournot–Bertrand duopoly model with heterogeneous goods and its complex characteristics , 2013 .

[8]  Tor Arne Johansen,et al.  Nonlinear Observer for Tightly Coupled Integration of Pseudorange and Inertial Measurements , 2016, IEEE Transactions on Control Systems Technology.

[9]  Junhai Ma,et al.  Study and Simulation on Discrete Dynamics of Bertrand Triopoly Team-Game , 2015 .

[10]  Junhai Ma,et al.  The Influence of Information Acquisition on the Complex Dynamics of Market Competition , 2016, Int. J. Bifurc. Chaos.

[11]  Marcella Scrimitore,et al.  Price or quantity? The strategic choice of subsidized firms in a mixed duopoly , 2013 .

[12]  Junhai Ma,et al.  Complex system and influence of delayed decision on the stability of a triopoly price game model , 2013 .

[13]  Junhai Ma,et al.  The influence of information on the stability of a dynamic Bertrand game , 2016, Commun. Nonlinear Sci. Numer. Simul..

[14]  Victor J. Tremblay,et al.  The Cournot–Bertrand model and the degree of product differentiation , 2011 .

[15]  X. Vives,et al.  Price and quantity competition in a differentiated duopoly , 1984 .