多目标博弈弱Pareto-Nash平衡点集的稳定性研究  

The Stability of the Weakly Pareto-Nash Equilibrium Points Set for Multi-objective Games

作　　者：李天成 宋奇庆[1] 

机构地区：[1]桂林理工大学理学院,广西桂林541004

出　　处：《杭州师范大学学报（自然科学版）》2017年第6期641-646,共6页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11661030);广西自然科学基金项目(2016GXNSFAA380059)

摘　　要：运用一致拓扑的方法研究了支付函数和策略集双重扰动下多目标博弈弱Pareto-Nash平衡点的稳定性,结果表明大多数多目标博弈的弱Pareto-Nash平衡点能够抵抗支付函数和策略集的双重扰动;证明了一定条件下弱Pareto-Nash平衡点的本质稳定连通区的存在性,推导出多目标优化问题弱有效解的本质连通区的存在性,推广了相应文献的结果.This article studies the stability of the weakly Pareto-Nash equilibrium points set for multi-objective games under the dual perturbations of payoffs and strategies using uniform topology. The results show that the weakly Pareto-Nash equilibrium point for most multi-objective games has the ability to resist these dual perturbations from payoff functions and strategy sets. Furthermore, the existence of essential connected components of weakly Pareto-Nasb equilibrium points is proved under some conditions. And the existence of essential connected components of weak efficient solutions of a multi- objective optimization problem is deduced. These generalize the corresponding results in relevant references.

关 键 词：多目标博弈 弱Pareto-Nash平衡点 本质连通区 稳定性 

分 类 号：O177.91[理学—数学]