摘要
本文研究向量拟平衡问题,得到了向量拟平衡问题解的一个存在性结果,证明了在满足一定的连续性和凸性条件的问题构成的空间Y中,大多数(在Baire分类意义下)问题的解集是稳定的,并证明Y的某子集中,每个向量拟平衡问题的解集中至少存在一个本质连通区。作为应用,我们导出了多目标广义对策弱Pareto-Nash平衡点的存在性,证明了在满足一定的连续性和凸性条件的多目标广义对策构成的空间P中,大多数对策的弱Pareto-Nash平衡点是稳定的,并证明了P中的每个对策的弱Pareto-Nash平衡点集中至少有一个本质连通区。
In this paper, we study the vector quasi-equilibrium problems. An existence theorem is obtained. We prove that, in the space Y consisting of vector quasi-equilibrium problems (satisfying some continuity and convexity conditions), most problems (in the sense of Baire category) have stable solution sets, and in a subset of Y, every problem possesses at least one essential component of its solution set. As applications, we derive an existence theorem of weak Pareto-Nash equilibrium points for multiobjective generalized games. Moverover, we show that, in the space P consisting of multiobjective generalized games (satisfying some continuity and convexity conditions), most games (in the sense of Baire category) have stable weak Pareto-Nash equilibrium point sets and every game in P has at least one essential component of its weak Pareto-Nash equilibrium point set.
出处
《系统科学与数学》
CSCD
北大核心
2004年第1期74-84,共11页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(10061002)
贵州省自然科学基金
贵州大学优秀人才科研基金