摘要
引入了集值映射不动点在图象意义下的Tikhonov良定性概念.此概念是Lemaire等提出的单值映射不动点概念以及Yang和Yu提出的集值映射不动点概念在映射值意义下的Tikhonov良定性的改进.然后给出了判定Tikhonov良定性的在紧性条件下的一个充分条件和在非紧n维实空间下的充要条件.同时,也给出了广义集值映射不动点在图象意义下的Tikhonov良定性概念及相应的判定条件.最后,作为在对策论中的应用,导出了n人有限非合作对策关于Nash平衡点和n人非合作多目标对策关于弱Pareto-Nash平衡点的Tikhonov良定性.
The authors first introduce the notion of Tikhonov well-posedness of set-valued mappings for fixed points under graph, which is an inprovement of Tikhonov well-posedness of single-valued mappings for fixed points under values in Lemaire et al. and that of set-valued mappings for fixed points under values in Yang and Yu. Then they provide a sufficient condition for Tikhonov well-posedness of set-valued mappings for fixed points under graph in the setting of compactness and give a full characterization of it in the setting of Rn. And then the notion of generalized Tikhonov well-posedness for fixed points with some properties is given. As applications to game theory, they study the Tikhonov well-posedness of best reply correspondences for Nash equilibrium points and that of best reply correspondences for weakly Pareto-Nash equilibrium points.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第4期774-778,共5页
Journal of Sichuan University(Natural Science Edition)
基金
贵州省教育厅自然科学研究基金(黔科合丁字[2007]2007号)
贵州师范大学博士研究基金(2006)
