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

页码：571 / 605

页数：35

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