混合双寡头Bertrand博弈模型的复杂动态性研究  

Complex Dynamics Analysis of a Mixed Duopoly Bertrand Game Model

作　　者：焦琳致 包振华[2] JIAO Linzhi;BAO Zhenhua(Basic Courses Teaching and Research Department,YingKou Institute of Technology,Yingkou 115100,Liaoning,China;School of Mathematics,Liaoning Normal University,Dalian 116081,Liaoning,China)

机构地区：[1]营口理工学院基础教研部,辽宁营口115100 [2]辽宁师范大学数学学院,辽宁大连116081

出　　处：《汕头大学学报(自然科学版)》2025年第1期72-80,共9页Journal of Shantou University:Natural Science Edition

基　　金：辽宁省教育厅基本科研项目(JYTMS20231043)。

摘　　要：考虑国有企业和私营企业混合竞争的价格博弈模型,他们共同生产某种差异化商品,并且采用有限理性预期原则确定商品的未来价格.建立二维离散动力系统,求解动力系统的边界均衡点和纳什均衡点,并研究它们的稳定性.在数值分析中,通过分岔图、最大Lyapunov指数、奇异吸引子和对初始条件的敏感依赖展示系统的动态性质.最后,利用反馈控制策略对系统进行混沌控制,使系统最终趋于稳定.In this paper,a price game model is considered for mixed competition between state-owned enterprises and private enterprises,which produce a differentiated goods together,and determine the future price of the goods by using the principle of bounded rational expectation.A two-dimensional discrete dynamical system is established,and the boundary equilibrium point and Nash equilibrium point of the dynamical system are solved,and their stability is studied.In numerical analysis,the dynamics of the system are demonstrated through bifurcation diagram,maximum Lyapunov exponent,the strange attractor,and sensitive dependence on initial conditions.Finally,the state variables feedback and parameter variation can be used to control the chaos of the system,which makes the system ultimately stable.

关 键 词：混合竞争 BERTRAND博弈 纳什均衡点 稳定性 混沌控制 

分 类 号：F224[经济管理—国民经济] O29[理学—应用数学]