Stability of Weakly Pareto-Nash Equilibria and Pareto-Nash Equilibria for Multiobjective Population Games

被引：28

作者：

Yang, Guanghui ^{[1
]}

Yang, Hui ^{[1
]}

机构：

[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Peoples R China

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2017年 / 25卷 / 02期

基金：

美国国家科学基金会;

关键词：

Stability; Generic continuity; Multiobjective population games; Pareto-Nash equilibrium; Sub-mapping; OPTIMIZATION PROBLEMS; ESSENTIAL COMPONENTS; GENERALIZED GAMES; SET; POINTS;

D O I：

10.1007/s11228-016-0391-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the method of generic continuity of set-valued mappings, this paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibria for multiobjective population games, when payoff functions are perturbed. More precisely, the paper investigates the continuity properties of the set of weakly Pareto-Nash equilibria and that of the set of Pareto-Nash equilibria under sufficiently small perturbations of payoff functions. Firstly, the set of weakly Pareto-Nash equilibria is proven to be upper semicontinuous and further generically continuous with the perturbed payoff functions. Secondly, examples are illustrated to show that the set of Pareto-Nash equilibria is neither upper semicontinuous nor lower semicontinuous. By seeking an upper semicontinuous sub-mapping, it is shown that the set of Pareto-Nash equilibria is partly upper semicontinuous and almost lower semicontinuous.

引用

页码：427 / 439

页数：13

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