广西师范大学学报（自然科学版） ›› 2025, Vol. 43 ›› Issue (6): 140-151.doi: 10.16088/j.issn.1001-6600.2024090304

• 数学与统计学 • 上一篇    下一篇

异质决策下具有延迟结构和随机成本的Cournot博弈动力学分析

许迪, 杨光惠*   

  1. 贵州大学 数学与统计学院,贵州 贵阳 550025
  • 收稿日期:2024-09-03 修回日期:2025-01-06 发布日期:2025-11-19
  • 通讯作者: 杨光惠(1976—),女(苗族),贵州贵阳人,贵州大学教授,博士。E-mail: ghuiyang@126.com
  • 基金资助:
    贵州省科技计划项目(黔科合基础-zk〔2025〕面上676)

Dynamic Analysis of Cournot Game with Delay Structure and Random Cost under Heterogeneous Decision-making

XU Di, YANG Guanghui*   

  1. School of Mathematics and Statistics, Guizhou University, Guiyang Guizhou 550025, China
  • Received:2024-09-03 Revised:2025-01-06 Published:2025-11-19

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摘要： 本文首先建立具有随机成本的动态Cournot博弈模型;然后,基于延迟和梯度调整的异质决策机制建立相应非线性动力系统,进一步求解该系统平衡点并分析Nash均衡点的稳定性;最后,通过数值仿真,研究延迟参数、产品差异参数以及随机变量等对系统稳定性的影响。本文结论如下:①延迟参数对系统稳定性的影响非单调,随着延迟参数的增加,系统稳定区域先增加,当延迟参数增加到一定程度后,系统的稳定性逐渐减弱;②随机变量越大,系统的稳定性也越强;③两局中人对初始值扰动敏感程度不同,具有延迟理性行为的局中人抗初始值扰动能力更强。

关键词: Cournot博弈, 时间延迟, 随机成本, 非线性动力系统, 异质决策

Abstract: A dynamic Cournot game model with random cost is constructed. Based on the heterogeneous decision-making mechanisms of delay and gradient adjustment, the corresponding nonlinear dynamic system is established. Furfthermore, the equilibrium points of the system are solved and the dynamical stability of the Nash equilibrium point is analyzed.Through numerical simulation, the effects of the delay parameter, the product difference parameter and the random variable on system stability are studied. The conclusions are as follows. Firstly, the effect of the delay parameter on the stability of the system is non-monotonic. With the increase of the delay parameter, the stable region of the system is widened, but when the delay parameter increases to a certain extent, the stability of the system gradually weakens. Secondly, the larger the random variable is, the stronger the stability of the system is. Finally, the sensitivity of two players to the initial value disturbance is different, and the one with delayed rational behavior has stronger ability to resist the initial value disturbance.

Key words: Cournot game, time delay, random cost, nonlinear dynamical systems, heterogeneous decision-making

中图分类号:  O225

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