多目标博弈加权纳什平衡点集的通用稳定性

在多目标博弈加权纳什平衡理论基础下,讨论多目标博弈在向量值支付函数伪连续条件下加权纳什平衡点的存在性结果;构建伪连续向量值支付函数的博弈空间,给出加权纳什平衡点的定义,同时定义多目标博弈的集值映射,并证明集值映射是非空的、凸的、usco映射;应用Fan-Glicksberg不动点定理、Fort定理以及本质平衡点的定义,讨论权向量和支付函数及策略集三者同时扰动下加权纳什平衡点的通有稳定性情况,得出在Baire分类意义下,构造的问题是本质的,也即是多目标博弈的加权纳什平衡点具有通有稳定性。

Generic Stability of Weighted Nash Equilibrium Point Sets in Multi-objective Games

Based on the theoretical basis of weighted Nash equilibrium in multi-objective games, the existence results of weighted Nash equilibrium points in multi-objective games under the condition that the vector-valued payoff function was pseudo-continuous were discussed. The game space of pseudo continuous vector-valued payment function was constructed, the definition of weighted Nash equilibrium point was given, and the set-valued mapping of multi-objective game was defined, and the set-valued mapping was proved to be non-empty, convex and USCO mapping. By using Fan-Glicksberg fixed point theorem, Fort theorem and the definition of intrinsic equilibrium point, the generic stability of weighted Nash equilibrium point was discussed under simultaneous perturbation of weight vector, payment function and strategy set. It is concluded that in the sense of Baire''s classification, the problem we construct is essential, that is, the weighted Nash equilibrium points in multi-objective games have generic stability.