两阶段服务博弈模型的复杂动力学行为分析

Complex Dynamic Behavior Analysis of Two-stage Service Game Model

采用梯度调整机制建立了一个具有有限理性的两阶段动态服务博弈双寡头模型,并对该模型进行动力学分析.利用相关平衡点Jacobian矩阵特征值的大小讨论了系统3个边界均衡点的类型及稳定性,利用Jury判据得到唯一Nash均衡点的局部稳定性条件.由1-D分岔图、最大Lyapunov指数、2-D分岔图分析了系统的复杂动力学行为,对借助数值模拟所刻画的吸引盆和吸引子的演化过程进行了全局动力学分析.结果表明,系统主要通过flip分岔的方式由稳定状态陷入混沌;并且随着调整速度的增大,吸引子与其吸引盆边界接触发生全局分岔;另外,吸引子的数目和结构也因调整速度的变化而变化,同时系统由稳定转向不稳定.因此,企业应当控制好调整速度,做出合理决策,避免陷入市场混乱.

A two-stage dynamic service game duopoly model with bounded rationality is establied by using the gradient adjustment mechanism,and the dynamic analysis of the model is carried out.The types of three boundary equilibrium points and their stability are discussed by using the eigenvalues of Jacobian matrices for relevant equilibrium points.According to the conditions related to local stability of the unique Nash equilibrium point are obtained from the Jury criterion.The complex dynamical behavior of system is analyzed based on the 1-D bifurcation diagrams,the largest Lyapunov exponent,and well as 2-D bifurcation diagrams.The global dynamic analysis is carried out by the evolution process of basins of attraction and attractors described by numerical simulation.The results indicate that the system goes from stability to chaos mainly via flip bifurcation.Moreover,with the increase of adjustment speed,the global bifurcation occurs when the attractor contacts with the boundary of its basin of attraction.In addition,the number and structure of attractors also change due to the change of the adjustment speed,and the system changes from stable to unstable.Therefore,enterprises should control the adjustment speed and make reasonable decisions to avoid falling into market chaos.