在线阅读 --自然科学版 2021年1期《广告双寡头博弈模型的数值分析》
广告双寡头博弈模型的数值分析--[在线阅读]
张莉莉, 周伟
兰州交通大学 数理学院, 甘肃 兰州 730070
起止页码: 8--14页
DOI: 10.13763/j.cnki.jhebnu.nse.202101002
摘要
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.

Numerical Analysis of Advertising Duopoly Game Model
ZHANG Lili, ZHOU Wei
School of Mathematics and Physics, Lanzhou Jiaotong University, Gansu Lanzhou 730070, China
Abstract:
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.

收稿日期: 2020-08-20
基金项目: 国家自然科学基金(61863022);中国博士后科学基金(2017M623276)

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