English

运筹学学报

• 运筹学 • 上一篇    下一篇

可行策略对应的图像拓扑下广义博弈Nash平衡的稳定性

陈拼博1   王能发1,2,*  丘小玲1  王春1   

  1. 1. 贵州大学数学与统计学院, 贵阳  550025 2. 贵州财经大学数学与统计学院, 贵阳 550025
  • 收稿日期:2015-12-14 出版日期:2017-09-15 发布日期:2017-09-15
  • 通讯作者: 王能发 155064857@qq.com
  • 基金资助:

    国家自然科学基金(No. 61472093), 贵州省教育厅自然科学基金(No. 黔教合KY字[2015]421), 贵州大学研究生创新基金(No. 2016017)

The stability of Nash equilibria for generalized games under graph topology of feasible strategy correspondence

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

  1. 1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China 2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
  • Received:2015-12-14 Online:2017-09-15 Published:2017-09-15

PDF

239

摘要：

以往关于广义博弈Nash平衡的稳定性的研究, 均利用可行策略映射之间的一致度量. 现考虑在更弱的度量下, 利用可行策略映射图像之间的Hausdorff距离定义度量.
在此弱图像拓扑下, 证明了广义博弈空间的完备性, 以及Nash平衡映射的上半连续性和紧性, 进而得到广义博弈Nash平衡的通有稳定性. 即在Baire分类的意义下,
大多数的广义博弈都是本质的.

关键词: 广义博弈, 可行策略映射, 图像拓扑, Nash平衡, 通有稳定性

Abstract:

For the stability of generalized games' Nash equilibria, current researches are investigated by uniform metric topology of feasible strategy correspondence. However, this paper presents a weaker metric and uses Hausdorff distance of graph of feasible strategy correspondence to study the stability of Nash equilibria. Under weaker graph topology, we prove that the space of generalized games is complete, and Nash equilibrium correspondence is upper semi-continuous and compact-valued. These lead to generic stability of generalized games' Nash equilibria, i.e., in the sense of Baire category, most of generalized games are essential.

Key words: generalized games, feasible strategy correspondence, graph topology, Nash equilibria, generic stability