基于相对利润最大化下的非对称量子Cournot博弈的动力学分析  

Kinematic analysis of asymmetric quantum Cournot game based on relative profit maximization

作　　者：邓智艺 DENG Zhiyi(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou,Gansu 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《内江师范学院学报》2024年第4期13-19,25,共8页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(61863022)。

摘　　要：针对相对利润最大化下的非对称量子Cournot博弈模型进行了分析,旨在研究经济系统中的复杂行为和决策过程.引入了量子纠缠的概念,并结合非对称的需求函数和成本函数,探索了企业之间的动态互动和策略选择.通过建立动态博弈模型,揭示了系统的演化过程和稳定性条件,分析了量子纠缠度以及非对称的需求函数和成本函数对纳什均衡点稳定性和复杂动力行为的影响.数值模拟表明当固定其他参数时,较小的调整速度可以使市场环境保持相对稳定.而量子纠缠度可以增强系统的稳定性,当企业产量调整速度过大时,会导致系统呈现复杂的混沌特性,而量子纠缠度可以有效地控制混沌状态的出现.最后,比较了非对称性对均衡解以及稳定性的影响.The asymmetric quantum Cournot game model under relative profit maximization is analyzed,of which the aim is to study complex behaviors and decision-making processes in economic systems.The concept of quantum entanglement is introduced,and in combination with asymmetric demand functions and cost functions,the dynamic interactions and strategy choices between enterprises are explored.By establishing a dynamic game model,the evolution process and stability conditions of the system are revealed.The effects of quantum entanglement and asymmetric demand and cost functions on the stability of the Nash equilibrium point and complex dynamic behavior are examined.Numerical simulations show that when other parameters are fixed,a smaller adjustment speed can keep the market environment relatively stable.Quantum entanglement can enhance the stability of the system.When the company’s output adjustment speed is too large,it will cause the system to exhibit complex chaotic characteristics,and quantum entanglement can effectively prevent the emergence of chaotic states.Finally,the effects of asymmetry on equilibrium solutions and stability are compared.

关 键 词：相对利润最大化 非对称双寡头博弈 量子纠缠 分岔 多稳态运动 

分 类 号：O225[理学—运筹学与控制论]