OPTIMAL CONTROL AND ZERO-SUM GAMES FOR MARKOV CHAINS OF MEAN-FIELD TYPE

被引：6
|
作者：
Choutri, Salah Eddine [1 ]
Djehiche, Boualem [1 ]
Tembine, Hamidou [2 ]
机构：
[1] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
[2] NYU, Learning & Game Theory Lab, 19 Washington Sq North, New York, NY 10011 USA
来源：
MATHEMATICAL CONTROL AND RELATED FIELDS | 2019年 / 9卷 / 03期
基金：
瑞典研究理事会;
关键词：
Mean-field; nonlinear Markov chain; backward SDEs; optimal control; zero-sum game; saddle point; stochastic maximum principle; thinning; LARGE DEVIATIONS; LARGE NUMBERS; EXISTENCE; SYSTEMS; BSDES; LAW;
D O I：
10.3934/mcrf.2019026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type.
引用
收藏
页码：571 / 605
页数：35
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