基于“价格差”策略的Bertrand双寡头博弈模型演化分析  

On Bertrand Duopoly Game Model Based on “Price Difference” Strategy

作　　者：周心莲 杜明娟 ZHOU Xin-lian;DU Ming-juan(School of Maths and Computer Science,Hanjiang Normal University,Shiyan 442000,China;School of Finance,Nanjing Audit University,Nanjing 211815,China)

机构地区：[1]汉江师范学院数学与计算机科学学院,湖北十堰442000 [2]南京审计大学金融学院,江苏南京211815

出　　处：《汉江师范学院学报》2023年第3期18-22,共5页Journal of Hanjiang Normal University

基　　金：湖北省教育厅科研项目“基于动力学理论的经济、金融系统建模与分析”(项目编号:B2018216)。

摘　　要：在寡头博弈模型中,由于厂商无法得到充分的信息,只有在有限理性的基础上根据“边际利润”或“边际效用”来定产定价.通过引入“价格差”这一影响决策的重要因素,研究了双寡头Bertrand博弈模型均衡解的稳定性、分叉图、最大李雅普诺夫指数图等动力学演化行为.研究结果表明,引入“价格差”后的动态博弈系统对厂商的调整系数更为敏感,当厂商调整速度较小变化时,系统便会出现分叉、混沌等一系列复杂动力学现象.因此,厂商如何避免价格变化对企业稳健的影响是经济、金融风险管理中的重要工作.In the oligopoly model, marginal profit or marginal utility is often used to decide the fixed price and output due to that the firms are unable to get sufficient information. By introducing “price difference” as an important factor influencing the decision making, the authors study the stability evolution of the duopoly Bertrand game, including the stability of the equilibrium solution, bifurcation diagram and the maximum Lyapunov exponent diagram. The results show that the dynamic game system after the introduction of the “price difference” is more sensitive to the firm's adjustment parameter. When the speed of adjustment is slow, a series of complex dynamic phenomena such as bifurcation and chaos will appear. Therefore, how to avoid the impact of price changes on the firm is an important part in the management of economical and financial risks.

关 键 词：BERTRAND模型 价格差 分叉 混沌控制 

分 类 号：F224[经济管理—国民经济]