政府征税与补贴Bertrand博弈模型的动力学分析

在政府同时实施征税与补贴政策的背景下,基于有限理性建立了动态Bertrand博弈模型。利用Jury条件分析了系统平衡点的局部渐近稳定性,均衡点失稳后系统的演化过程采用数值模拟的方法进行讨论。讨论发现,企业利润在Nash均衡态最优,价格调整速度过高或政府给予的补贴份额过低均使系统进入混沌,企业利润将出现负增长。为了保证企业处于盈利模式,采用状态反馈和参数调节控制策略使系统长期处于Nash均衡。此外,分析吸引盆内部结构发现,过高的调整速度使系统发生全局分岔,初始决策的选择出现不可预测性。

Dynamic analysis of Bertrand game model about taxation of government and subsidy

In the context of government implements both subsidy and taxation policies, a dynamics Bertrand game model is established based on bounded rationality. The local asymptotic stability of equilibrium points of the system is analyzed using Jury conditions, the evolution process of the system after equilibrium point instability is discussed by numerical simulation method. It is found that enterprise profit is optimal in Nash equilibrium. The high speed of price adjustment or the low share of government subsidies make the system chaotic, and the profits of enterprises will increase negatively. In order to ensure that enterprises are in the profit mode, the state feedback and parameter adjustment control strategy are adopted to keep the system in Nash equilibrium for a long time. In addition, by analyzing the internal structure of the attraction basin, it is found that the high adjustment speed makes the system bifurcate globally, and the choice of initial decision-making appears unpredictable.