Stability for Nash Equilibrium Problems

• 成果类型: Article
• 署名作者: Diao, Ruoyu; Dai, Yu-Hong; Zhang, Liwei
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Northeastern University - China; Northeastern University - China
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0609
• 发表日期: 2026-08
• 关键词: Nash equilibrium problems; strong regularity; continuously differentiable single-valued localization; robust isolated calmness; aubin property; strict Mangasarian-Fromovitz constraint qualification; quadratic programming; variational-inequalities

摘要

Consider the stability properties of the Karush-Kuhn-Tucker (KKT) solution mapping SKKT for Nash equilibrium problems (NEPs) with canonical perturbations. Firstly, we obtain an exact characterization of the strong regularity of SKKT as well as an easily verified sufficient condition. Secondly, we propose equivalent conditions for the continuously differentiable single-valued localization of SKKT. Thirdly, the isolated calmness of SKKT is studied based on the I-property. The P-property is proposed as a sufficient condition for the robust isolated calmness of SKKT under convex assumptions. Furthermore, we establish that studying the stability properties of the NEP with canonical perturbations is equivalent to studying those of the NEP with only tilt perturbations, based on the prior discussions. Finally, we provide detailed characterizations of stability for the NEPs in which each individual player solves a quadratic programming problem.