相对利润最大化下量子Bertrand博弈模型的动力学分析  

Dynamics Analysis of a Quantum Bertrand Game Model Based on Relative Profit Maximization

作　　者：郭丹丹 GUO Dan-dan(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵州贵阳550025

出　　处：《物流工程与管理》2024年第10期95-99,共5页Logistics Engineering and Management

摘　　要：文中考虑市场中两家企业都以相对利润最大化为目标,并采用梯度调节机制来进行策略调整,进而建立了一个基于相对利润最大化的有限理性动态量子Bertrand博弈模型。通过理论分析,得到了量子Nash均衡点的局部稳定性条件。此外,通过数值仿真,直观地呈现了均衡点随着各参数的动态演化过程。结果表明,当两家企业的调整速率和边际成本过高时,系统会通过分岔进入混沌状态,使市场变得不稳定;而较高的量子纠缠度可以延迟分岔和混沌的发生,有效控制市场的稳定。最后发现,企业产品的差异化程度过高或过低都会导致市场的不稳定,需要控制在合适范围内。In this paper,considering that the two firms regard relative profit maximization as the goal and use the gradient adjustment mechanism to make strategic adjustments,a bounded rational dynamic quantum Bertrand game model based on relative profit maximization is established.Through theoretical analysis,the local stability conditions of the quantum Nash equilibrium point are obtained.In addition,the dynamic evolution of the system with each parameter is presented visually through numerical simulation.The findings demonstrate that the system will become unstable as adjustment speed and marginal cost increase,but a higher degree of quantum entanglement can delay the occurrence of chaos and effectively control the emergence of chaos.Finally,it is found that the system keeps stable with an appropriate value of product differentiation.

关 键 词：BERTRAND模型 量子博弈 相对利润最大化 有限理性 

分 类 号：F224.32[经济管理—国民经济]