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运筹学学报 ›› 2016, Vol. 20 ›› Issue (3): 107-120.doi: 10.15960/j.cnki.issn.1007-6093.2016.03.012

• 运筹学 • 上一篇    下一篇

关于非凸的有限理性的稳定性

王春1  丘小玲1,*  王能发1,2 陈拼博1   

  1. 1. 贵州大学数学系, 贵阳 550025 2. 贵州财经大学数学与统计学院, 贵阳 550025
  • 收稿日期:2015-11-17 出版日期:2016-09-15 发布日期:2016-09-15
  • 通讯作者: 丘小玲 xlqiu@gzu.edu.cn
  • 基金资助:

    国家自然科学基金(Nos. 61472093, 11271098), 贵州省教育厅自然科学基金(No. 黔教合KY字[2015]421)

Stability to bounded rationality for nonconvexity

WANG Chun1  QIU Xiaoling1,*   WANG Nengfa1,2  CHEN Pinbo1   

  1. 1. Department of Mathematics, Guizhou University, Guiyang 550025, China 2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
  • Received:2015-11-17 Online:2016-09-15 Published:2016-09-15

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摘要：

关于有限理性方面的文献, 大多数都是在满足凸性条件下研究有限理性的相关性质, 在一定程度上限制了其应用范围. 应用Ekeland变分原理, 减弱了有限理性模型的假设条件, 考虑在不满足凸性条件下的有限理性模型的稳定性问题. 具体给出了非凸的Ky Fan点问题解的稳定性, 非凸非紧的Ky Fan点问题解的稳定性, 非凸向量值函数Ky Fan点解的稳定性和非凸非紧向量值函数Ky Fan点解的稳定性. 作为应用, 还给出了非凸的n人非合作博弈有限理性模型解的稳定性和非凸的多目标博弈有限理性模型解的稳定性.

关键词: 有限理性, Ekeland 变分原理, 稳定性, 非凸性, 平衡点

Abstract:

In recent years, there are many articles about bounded rationality. However, most articles study the properties of bounded rationality under the condition of convexity, and this leads to the limited scope of its application. This paper uses Ekeland variational principle and weaks the assumptions of bounded rationality. Under the condition of nonconvex  we study the stability of bounded rationality model problem. And the solution's stability of the nonconvex Ky Fan point problem, the solution's stability of the nonconvex and noncompact Ky Fan point problem, the solution's stability of the nonconvex Vector-valued function Ky Fan point problem and the solution's stability of the nonconvex and noncompact Vector-valued function Ky Fan point problem are given. As an application, we also give the solution's stability of the nonconvex n-person noncooperative games' bounded rationality model and the solution's stability of the nonconvex multi-objective games' bounded rationality model.

Key words: bounded rationality, Ekeland's variational principle, stability, nonconvexity, equilibrium point