考虑广告溢出效应的博弈模型的动力学分析

在有限理性的基础上,引入广告溢出效应、调整速度、广告促销效果等参数建立了有限理性的动态调整博弈模型。依据Jacobi矩阵的特征值和Jury判据讨论了系统的稳定性。通过单、双参数分岔图、最大Lyapunov指数图和吸引盆分析了系统在广告溢出效应、调整速度等参数下动态演化过程。结果表明,当广告溢出效应调整速度越低时,系统会处于更加稳定的状态,市场就处于平稳的状态。此外,当调整速度增大时,系统出现由周期进入混沌以及吸引子共存的现象,说明市场将会发生混乱。

Dynamic analysis of game model considering advertising spillover effect

Based on the bounded rationality, the dynamic adjustment game model of bounded rationality is established by introducing the parameters of advertising spillover effect, adjustment speed and advertising promotion effect. Firstly, the stability of the system is discussed based on the eigenvalues of Jacobi matrix and Jury criterion. Secondly, the dynamic evolution process of the system under the parameters of advertising spillover effect and adjustment speed is analyzed by the bifurcation diagram of single and double parameters, the maximum Lyapunov index diagram and the attractor basin. The results show that when the adjustment speed of advertising spillover effect is slower, the system will be in a more stable state, and will be in a stable state. In addition, when the adjustment speed increases, the system appears chaos from period and attractor coexistence, which indicates that the market will be chaotic.