策略委托下古诺双寡头博弈的动力学行为  

Dynamic Behavior in Cournot Duopoly Game with Strategic Delegation

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

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《咸阳师范学院学报》2023年第6期17-26,共10页Journal of Xianyang Normal University

基　　金：国家自然科学基金项目(11962011)。

摘　　要：在传统Cournot模型的基础上,建立了一个基于策略委托和相对利润的动态博弈模型。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,用数值模拟的方法,结合二维分岔图,研究了系统在不同参数空间下的稳定区域以及其中Arnold舌的排列规律,并利用吸引盆分析了一维分岔图中的非常规分岔现象及系统的全局分岔行为。研究表明,模型中的不同参数对系统稳定性有显著影响。委托系数越大,调整速度越小,在一定范围内边际成本越高,越有利于企业的发展。此研究对于深入了解Cournot竞争模型在动态博弈下的动力学行为具有重要意义。Based on the traditional Cournot model,a dynamic game model based on strategy delegation and relative profit is established,and the local stability of the equilibrium point of the system is analyzed by using the Jacobian matrix and Jury criterion.Second,through numerical simulation,combined with two-dimensional bifurcation diagram,a study was made of the stable region of the system under different parameter spaces and the arrangement of Arnold’s tongue and an analysis was made of the unconventional bifurcation phenomenon in the one-dimensional bifurcation diagram and the global bifurcation behavior of the system by using the basin of attraction.Studies have shown that various parameters in the model have a significant impact on the stability of the system.In particular,the larger the commission coefficient,the smaller the adjustment speed,and the higher the marginal cost within a certain range,the more conducive it is to the development of the enterprise.This study is of great significance for the in-depth understanding of the dynamic behavior of Cournot’s competitive model under dynamic games.

关 键 词：策略委托 分形舌 吸引子共存 全局分岔 

分 类 号：O415.5[理学—理论物理] F224.32[理学—物理]