English

运筹学学报 ›› 2013, Vol. 17 ›› Issue (3): 101-107.

• 运筹学 • 上一篇    下一篇

不确定性下强Berge均衡的存在性

邓喜才1,2,*，向淑文1，左羽2   

  1. 1. 贵州大学数学系，贵阳 550025 2. 贵州师范学院数学与计算机系，贵阳 550018
  • 出版日期:2013-09-15 发布日期:2013-09-15
  • 通讯作者: 邓喜才 E-mail:iamdengxicai@163.com
  • 基金资助:

    国家自然基金 (No. 11161008), 教育部博士点基金 (No. 20115201110002), 贵州省科学技术基金 (Nos. [2012]2289, [2013]2235)

Existence of strong Berge equilibrium under uncertainty

DENG Xicai1,2,*, XIANG Shuwen1, ZUO Yu2   

  1. 1. Department of Mathematics, Guizhou University, Gui Yang 550025, China 2. Department of Mathematics and Computer, GuiZhou Normal College, GuiYang 550018, China
  • Online:2013-09-15 Published:2013-09-15

PDF

634

被引次数

2

摘要： 在已知不确定参数变化的范围下，研究了非合作博弈与广义非合作博弈的强Berge均衡的存在性，基于强Berge均衡与不确定性下非合作博弈的强Nash均衡的概念，给出了不确定参数下非合作博弈与广义非合作博弈的强Berge均衡的定义，并利用Fan-Glicksberg不动点定理证明其存在性，最后用算例验证其可行性.

关键词: 非合作博弈, 广义非合作博弈, 不确定性, 强Berge均衡, 存在性

Abstract:  Under the assumption that the domain of the undetermined parameters is known, the existence of strong Berge equilibrium for non-cooperative games and generalized non-cooperative games are investigated. Based on the concept of strong Berge equilibrium and NS-equilibrium for non-cooperative games under uncertainty, the notions of strong Berge equilibrium for non-cooperative games and generalized non-cooperative games under uncertainty are defined. Further, the existence of the equilibrium for non-cooperative games and generalized non-cooperative games are proved by using Fan-Glicksberg fixed point theorem. Finally, a numeric example illustrates the feasibility of the proposed method.

Key words: non-cooperative games, generalized non-cooperative games, uncertainty, strong Berge equilibrium, existence

中图分类号: