弱伪连续向量值函数及其在多目标博弈中的应用  

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

作　　者：张广[1] 邬冬华[2] 高静 

机构地区：[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

出　　处：《运筹学学报》2015年第1期92-98,共7页Operations Research Transactions

基　　金：上海自然科学基金(No.09ZR1411100);上海市重点学科基金(No.S30104)

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.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 vectorvalued 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.

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 

分 类 号：O225[理学—运筹学与控制论]