ϵ-Nash mean-field games for stochastic linear-quadratic systems with delay and applications  

作　　者：Heping Ma Yu Shi Ruijing Li Weifeng Wang 

机构地区：[1]School of Science,Hubei University of Technology,Wuhan 430068,China [2]School of Science,Wuhan University of Technology,Wuhan 430070,China [3]School of Statistics and Mathematics,Guangdong University of Finance&Economics,Guangdong 528100,China [4]School of Mathematics and Statistics,South-Central Minzu University,Wuhan 430074,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2024年第3期389-404,共16页概率、不确定性与定量风险（英文）

基　　金：supported by the National Natural Science Foundation of China (Grant No.11801154);R.J.Li was supported by the Guangzhou Science and Technology Program Project Project (Grant No.202201011057);W.F.Wang was supported by the Natural Science Foundation of Hubei Province (Grant No.2023AFC006).

摘　　要：In this paper,we focus on mean-field linear-quadratic games for stochastic large-population systems with time delays.The ϵ-Nash equilibrium for decentralized strategies in linear-quadratic games is derived via the consistency condition.By means of variational analysis,the system of consistency conditions can be expressed by forward-backward stochastic differential equations.Numerical examples illustrate the sensitivity of solutions of advanced backward stochastic differential equations to time delays,the effect of the the population's collective behaviors,and the consistency of mean-field estimates.

关 键 词：Mean-field game Linear-quadratic problem Time delay Large-population ϵ-Nash equilibrium 

分 类 号：O175[理学—数学]