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.