向量拟平衡问题的本质解及解集的本质连通区

ESSENTIAL SOLUTIONS AND ESSENTIAL COMPONENTS OF SOLUTION SET OF VECTOR QUASI-EQUILIBRIUM PROBLEMS

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.