JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (7): 32-45.doi: 10.6040/j.issn.1671-9352.0.2020.293

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Complex dynamic analysis of the duopoly game under management delegation

ZHU Yan-lan1, ZHOU Wei1*, CHU Tong2, LI Wen-na1   

  1. 1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China;
    2. School of Law, Zhejiang University of Finance and Economics, Hangzhou 310018, Zhejiang, China
  • Published:2021-07-19

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Abstract: On the basis of the exponential inverse demand function and considering that the enterprise managers take the maximization of their own interests as the objective function, the Cournot dynamic oligopoly game model which is more in line with the actual market environment is established. Through calculation, the system has four equilibrium points, and their local stabilities are analyzed using nonlinear dynamics theory and Jury criterion. The influence of parameters such as the speed of adjusting, weight coefficient and marginal cost on the stability of the system and the evolution process of the system under the change of parameters are analyzed by one-dimensional bifurcation diagrams and two-dimensional bifurcation diagrams. Three kinds of intermittent chaos phenomena are found, and it is concluded that this is a way of self-regulation of the system. In addition, multistability of the system is discussed through the basin of attractive, and it is concluded that the selection of initial conditions will affect the final state of system.

Key words: exponential inverse demand function, management delegation, intermittent chaos, basin of attraction, stability analysis

CLC Number: 

  • O193
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