一类非线性经济博弈模型动力学分析

Dynamic Analysis of a Nonlinear Economic Game Model

研究了一类基于有限理性预期的Bertrand双寡头博弈模型,运用动力学分岔理论,讨论了系统平衡点的稳定性,并且通过数值模拟系统的分岔图、最大Lyapunov指数图、相图等动力学特性,定性地分析了系统的动力学行为.研究表明随着厂商价格调整速度的增大,系统经过一系列分岔进入了混沌运动状态.因此,通过合理控制系统的参数范围,可以使系统处于稳定的运动状态,可以为市场决策者提供一定的参考依据.

This paper studies a Bertrand duopoly game model based on bounded rationality,and using the dynamical bifurcation theory,the stability of equilibrium points of the system is discussed.Besides,through the numerical simulated system,such as the bifurcation diagrams,the largest Lyapunov exponents diagram,the phase portraits and so on,this paper qualitatively analyzes the dynamical behaviors of the system.The research reveals that with the increase of manufacturer＇s price adjustment speed,the system goes into a state of chaos movement through a series of bifurcation.So,through reasonably controlling the parameters of the system,the system can be made into a stable state of motion,which provides certain reference for decision-makers of market.