非合作线性随机微分博弈的通有稳定性  

Generic Stability of Noncooperative Linear Stochastic Differential Games

作　　者：胡作鹏 杨彦龙 HU Zuopeng;YANG Yanlong(College of Mathematics and Statistics,Guizhou University,Guiyang 550025)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《系统科学与数学》2023年第7期1878-1887,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(71961003);贵州省科技厅联合基金项目(黔科合LH字[2017]7223);贵州大学博士基金(贵大人基合字(2019)49)资助课题。

摘　　要：文章研究了一类非合作线性随机微分博弈的通有稳定性.先利用Ky Fan不等式证明了开环Nash均衡的存在性,然后利用集值分析理论及Fort定理,证明了由一类非合作线性随机微分博弈所构成的集合Y_(1)必存在一个稠密剩余集Q,且Q中的非合作线性随机微分博弈都是稳定的.结论表明,在Baire分类意义上,Y_(1)中的大多数博弈是稳定的,且Y_(1)中每一个非合作线性随机微分博弈能被一列本质的非合作线性随机微分博弈逼近.This paper studies the generic stability of a class of non-cooperative linear stochastic differential games and proved the existence of open-loop Nash equilibrium by using Ky Fan inequality,and then by using set-valued analysis theory and Fort theorem,this paper proved that the set Y_(1) composed of a class of noncooperative linear stochastic differential games must have a dense residual set Q,and the non-cooperative linear stochastic differential games in Q are stable.And each non-cooperative linear stochastic differential game in Y_(1) can be approximated by a series of essentially non-cooperative linear stochastic differential games.

关 键 词：线性随机微分博弈 集值映射 通有稳定性 纳什均衡 

分 类 号：O225[理学—运筹学与控制论]