基于相对利润最大化的Stackelberg博弈均衡点的稳定性
Stability of Equilibrium Points in Stackelberg Game Based on Relative Profit Maximization
摘要: Stackelberg博弈是寡头市场中典型的序贯非合作动态博弈模型，更贴合现实中寡头市场的竞争模式。以相对利润最大化为决策准则，研究Stackelberg博弈模型的动态稳定性问题。采用雅可比矩阵特征值分析方法，结合Jury判别条件，对该动态博弈系统的边界均衡点与纳什均衡点稳定性进行分析，给出了纳什均衡点的稳定条件。本研究丰富了相对利润最大化下寡头动态博弈的稳定性研究体系，为寡头市场的竞争策略制定与市场调控提供了理论参考。
Abstract: As a typical sequential non-cooperative dynamic game model in oligopoly markets, the Stackelberg game is more consistent with the characteristics of real oligopoly market competition. This paper takes relative profit maximization as the decision criterion to investigate the dynamic stability of the Stackelberg game model. The research adopts the eigenvalue analysis method of the Jacobian matrix and combines with the Jury criterion to systematically analyze the stability of the boundary equilibrium points and Nash equilibrium point of the dynamic game system, and explicitly derives the stability conditions of the Nash equilibrium point. The research results enrich the stability research system of oligopolistic dynamic games under relative profit maximization, and provide theoretical support and reference for the formulation of competition strategies and market regulation in oligopoly market.
文章引用：刘政澎. 基于相对利润最大化的Stackelberg博弈均衡点的稳定性[J]. 应用数学进展, 2026, 15(3): 387-392. https://doi.org/10.12677/aam.2026.153113

参考文献

[1] Naimzada, A. and Tramontana, F. (2010) Dynamic Duopoly Games with Heterogeneous Players. Journal of Economic Behavior & Organization, 73, 75-86.
[2] Xin, Y., Chen, L. and Zhang, J. (2020) Local Stability of a Nonlinear Discrete Stackelberg Duopoly Model. Nonlinear Dynamics, 99, 3081-3095.
[3] Böhnlein, T. and Harks, T. (2017) Stackelberg Scheduling Games with Convex Costs. Journal of Scheduling, 20, 289-304.
[4] Ahmadi, A., Roy, S., Mehrabbeik, M., Ghosh, D., Jafari, S. and Perc, M. (2023) The Dynamics of a Duopoly Stackelberg Game with Marginal Costs among Heterogeneous Players. PLOS ONE, 18, e0283757. [Google Scholar] [CrossRef] [PubMed]
[5] Chen, L., Zhou, P. and Xiao, H. (2023) Backward Stackelberg Games with Delay and Related Forward-Backward Stochastic Differential Equations. Mathematics, 11, Article No. 2898. [Google Scholar] [CrossRef] 
[6] Liu, J., Wang, W., Xu, J. and Zhang, H. (2023) Stackelberg Strategy of Two-Player Stochastic Difference Game with Time Delay. International Journal of Control, Automation and Systems, 21, 2904-2915. [Google Scholar] [CrossRef] 
[7] Ma, H., Wang, Y. and Liu, X. (2023) Stability Analysis of a Delayed Bertrand Duopoly Game with Relative Profit Maximization. Communications in Nonlinear Science and Numerical Simulation, 118, Article ID: 106892.
[8] Zha, M., Li, X. and Yang, L. (2020) Spillover Effects on the Stability of Oligopoly Games with Relative Profit Maximization. Economic Modelling, 87, 364-375.
[9] Askar, S.S. and Al-khedhairi, A. (2020) Dynamic Investigations in a Duopoly Game with Price Competition Based on Relative Profit and Profit Maximization. Journal of Computational and Applied Mathematics, 367, Article ID: 112464. [Google Scholar] [CrossRef] 
[10] Wei, Z., Tan, W., Elsadany, A.A. and Moroz, I. (2023) Complexity and Chaos Control in a Cournot Duopoly Model Based on Bounded Rationality and Relative Profit Maximization. Nonlinear Dynamics, 111, 17561-17589. [Google Scholar] [CrossRef] 

为你推荐