广告双寡头博弈模型的数值分析

Numerical Analysis of Advertising Duopoly Game Model

在有限理性的基础上,构建了一个双寡头广告博弈模型,并求解其均衡点.通过稳定性理论分析了均衡点的局部稳定性.另外,对系统进行数值仿真分析通过改变产量调整速度会产生分岔、混沌等动力学现象,得到随着调整速度的逐渐增大,系统经历稳定状态、分岔状态最后进入混沌态.系统处于周期状态证明企业发展良好,而混沌态说明市场处于无序状态,这种情形不是制造商所期望的,因此,制造商只有将调整速度控制在一定范围内,选择最优的广告投入来促进产品销量增加才能达到自身利润最大化的目的.

On the basis of bounded rationality,a game model of duopoly advertising is constructed and its equilibrium points are solved.Local stability of equilibrium points are analyzed by stability theory.In addition,numerical simulation analysis of the system will produce bifurcation,chaos and other dynamic phenomena when the speed of output adjustment is changed.It is concluded that the system will respective­ly experience stable state,bifurcation state and finally enter into chaos state as the adjustment speed increa­ses gradually.The system is in the stage state,which proves that the enterprise develops well.Chaos sug­gests that the market is disordered,in which case it is not what the manufacturers had expected.Therefore,manufacturers should control the speed in a certain range,so that manufacturers can choose the optimal amount of advertising input to promote the increase of product sales,in order to achieve their own profit maximization.