等弹性需求下双寡头博弈的演化机制研究  

Research on the evolution mechanism of duopoly game under equal elastic demand

作　　者：吴怡晓 褚衍东[1] WU Yixiao;CHU Yandong(Lanzhou Jiaotong University,School of Mathematics and Science,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《商丘师范学院学报》2024年第12期6-13,共8页Journal of Shangqiu Normal University

摘　　要：在等弹性需求和二次成本函数的基础上,建立了基于策略委托和相对利润的二维动态博弈模型.首先用Jacobian矩阵及Jury判据对系统均衡点的局部稳定性进行了分析.其次,采用数值模拟的方法讨论了系统中的不同参数对于系统稳定性的影响,即调整速度和委托系数越小,边际成本在合理范围内时,系统越稳定,对企业的发展越有利.同时,研究发现,二维分岔图中,Arnold舌的排列规律与Stern-Brocot周期树的排列规律一致.除此之外,还给出了使得系统避免全局分岔现象产生的参数阈值.对于深入了解等弹性需求下,寡头动态博弈模型中的动力学行为具有重要意义.Based on the equal elastic demand and secondary cost function,a two-dimensional dynamic game model based on strategy delegation and relative profit is established.Firstly,the local stability of the equilibrium point of the system is analyzed by using the Jacobian matrix and Jury criterion.Secondly,the influence of different parameters in the system on the stability of the system is discussed by numerical simulation,that is,the smaller the speed of adjustment and commission coefficient,the more stable the system is within a reasonable range,the more favorable it is to the development of the enterprise.At the same time,it is found that the arrangement of c in the two-dimensional bifurcation diagram is consistent with the arrangement of the Stern-Brocot periodic tree.In addition,the study also gives parameter thresholds that allow the system to avoid global bifurcation.This study is of great significance for understanding the dynamic behavior in oligopoly dynamic game models under elastic demand.

关 键 词：等弹性需求 策略委托 多稳态 全局分岔 

分 类 号：O415.5[理学—理论物理] F224.32[理学—物理]