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运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (1): 235-246.doi: 10.15960/j.cnki.issn.1007-6093.2026.01.017

• • 上一篇    

KKMS点的稳定性研究

崔瑞琦, 张舒, 宋奇庆†   

  1. 山西师范大学数学科学学院, 山西太原 030000
  • 收稿日期:2022-08-02 发布日期:2026-03-16
  • 通讯作者: 宋奇庆 E-mail:songqiqing@126.com
  • 基金资助:
    国家自然科学基金 (No. 11661030), 山西省回国留学人员科研资助项目 (No. 2024-086)

The study of the stability of KKMS points

CUI Ruiqi, ZHANG Shu, SONG Qiqing†   

  1. School of Mathematical Science, Shanxi Normal University, Taiyuan 030000, Shanxi, China
  • Received:2022-08-02 Published:2026-03-16

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摘要： KKMS 定理是著名的Sperner引理的推广,在合作博弈论的各类核的存在性研究和数理经济学中的均衡分析中, KKMS定理都发挥着重要的基础性作用。基于KKMS定理在博弈论与经济学应用中的重要性, 本文引入了KKMS点的概念,构建了KKMS映射空间, 研究了KKMS点的稳定性, 得到了KKMS映射的半连续性和连续性结果。研究表明KKMS映射具有上半连续性。通过在2-单形中举出具体的反例, 进而表明KKMS映射一般不具有下半连续性, 并给出了该映射连续的充分必要条件,得出了KKMS点具有通有稳定性和本质稳定性, 结果包含了现有关于KKM点的相关稳定性结果。

关键词: KKMS引理, 均衡集, 通有稳定性, 连续性

Abstract: KKMS Theorem is the generalization of the famous Sperner Lemma. In the study of existence of many kinds of cores in cooperative game theory, and in the equilibrium analysis of mathematical economics, KKMS Theorem plays an important and fundamental role. Based on the importance of KKMS Theorem in the application of game theory and economics, this paper introduces the conception of KKMS points, constructs the space of KKMS mappings, and studies the stability of the KKMS points, and obtains the semi-continuous and continuous results of KKMS mappings. The results show that KKMS mappings have upper semi-continuity. Further, by constructing a specific counterexample in 2-simplices, this shows that KKMS mappings do not have lower semi-continuity generally. This also gives a sufficient and necessary condition for the continuity of KKMS mappings. Furthermore, this obtains that the KKMS points have generic stability and essential stability, which includes the existing stability results on KKM points as special cases.

Key words: KKMS Lemma, balanced sets, generic stability, continuity

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