延迟有限理性条件下Stackelberg-Bertrand博弈的动力学分析

Dynamic Analysis of Stackelberg-Bertrand Game under Delayed Bounded Rationality Conditions

基于双寡头Stackelberg-Bertrand纳什均衡稳定性问题,利用非线性动力学理论,构建延迟有限理性预期下的动态Stackelberg-Bertrand竞争模型,分析博弈模型均衡解的稳定性及失稳后的非线性动态演化特征。从分岔、最大Lyapunov指数、奇怪吸引子及初始条件敏感性方面进一步进行数值仿真验证。结果表明:延迟有限理性比一般有限理性更有利于增强系统的稳定性,且随着延迟系数的增大,系统的稳定性逐渐增强。

Based on the stability problem of the double oligopoly Stackelberg-Bertrand Nash equilibrium,a dynamic Stackelberg-Bertrand competition model under delayed finite rational expectations was constructed by using nonlinear dynamics theory and the stability of the equilibrium solution of the game model and the nonlinear dynamic evolution characteristics after instability were analyzed.The numerical simulations were carried out to verify the theory from the aspects of bifurcation,largest Lyapunov exponent,strange attractor and initial condition sensitivity.The results indicated that the delay bounded rationality was more conducive to enhancement of the stability of the system than that of the general bounded rationality,moreover,the stability of the system gradually increased with the increase of the delay coefficient.