弱伪连续向量值函数及其在多目标博弈中的应用

运筹学学报 ›› 2015, Vol. 19 ›› Issue (1): 92-98.

弱伪连续向量值函数及其在多目标博弈中的应用

张广¹, 邬冬华^2,*, 高静³

1. 上海大学管理学院, 上海 200444; 2. 上海大学数学系, 上海 200444; 3. 马陆育才联合中学, 上海 201801

收稿日期:2013-12-19 出版日期:2015-03-15 发布日期:2015-03-15
通讯作者: 邬冬华 E-mail:dhwu@staff.shu.edu.cn
基金资助:
上海自然科学基金(No. 09ZR1411100), 上海市重点学科基金(No. S30104)

The weakly pseudocontinuous of vector-valued functions and the application in multi-objective games

ZHANG Guang¹, WU Donghua^2,*, GAO Jing³

1. School of Management, Shanghai University, Shanghai 200444, China; 2. Department of Mathematics, Shanghai University, Shanghai 200444, China; 3. Malu Yucai Joint Middle School, Shanghai 201801, China

Received:2013-12-19 Online:2015-03-15 Published:2015-03-15

摘要/Abstract

摘要： 基于对弱伪连续实值函数的研究, 提出向量值函数关于锥的弱伪连续定义, 并建立了向量值函数$R_+^k$弱伪连续与实值函数弱伪连续的对应关系. 作为弱伪连续向量值函数的应用, 给出了弱伪连续下的向量值Ky Fan点的存在性定理, 并通过该定理证明了伪连续向量值支付下的多目标博弈弱Pareto-Nash平衡点的存在性定理.

关键词: 弱伪连续, 向量值函数, 向量值函数Ky Fan点, 多目标博弈

Abstract: In this paper, based on the study of pseudocontinuous real-valued functions, a definition of the weakly pseudocontinuous of vector-valued functions on cone is proposed. And a weakly pseudocontinuous relationship is established between the vector-valued functions on $R_+^k$ and the real-valued functions. As an application of the weakly pseudocontinuous of vector-valued functions on cone, the existence theorem of weakly Pareto-Nash equilibrium in multi-objective games with the pseudocontinuous payoffs is proved by the improved vector-valued Ky Fan points.

Key words: weakly pseudocontinuous, vector-valued functions, vector-valued Ky Fan points, multi-objective games

中图分类号:

O225

张广, 邬冬华, 高静. 弱伪连续向量值函数及其在多目标博弈中的应用[J]. 运筹学学报, 2015, 19(1): 92-98.

ZHANG Guang, WU Donghua, GAO Jing. The weakly pseudocontinuous of vector-valued functions and the application in multi-objective games[J]. Operations Research Transactions, 2015, 19(1): 92-98.

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