管理委托下的双寡头博弈的复杂动力学分析

在具有指数型逆需求函数的基础上,考虑企业管理者以自身利益最大化为目标函数,建立更符合实际市场环境的古诺动态双寡头博弈模型。通过计算得到系统存在4个均衡点,并利用非线性动力学理论和Jury判据对其进行了局部稳定性分析。通过一维和二维分岔图分析了调整速度、权重系数和边际成本对系统稳定性的影响以及系统在参数变化下的演化过程;并发现了3种间歇混沌现象,结论是其为系统进行自我调节的一种方式;此外,通过吸引盆讨论了系统的多稳态性,得出初始条件的选择会影响系统最终的状态。

Complex dynamic analysis of the duopoly game under management delegation

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.