On classical solutions to the mean field game system of controls

被引：19

作者：

Kobeissi, Ziad ^{[1
,2
,3
,4
,5
]}

机构：

[1] Univ Paris, CNRS, Lab Jacques Louis Lions LJLL, F-75006 Paris, France

[2] Sorbonne Univ, F-75006 Paris, France

[3] Inst Louis Bachelier, Paris, France

[4] INRIA Paris, Paris, France

[5] Univ Paris, Inst Louis Bachelier Paris, INRIA Paris, Lab Jacques Louis Lions LJLL, Paris, France

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 47卷 / 03期

关键词：

Mean field games; interactions through the law of states and controls; system of coupled PDEs; EXISTENCE; BEHAVIOR;

D O I：

10.1080/03605302.2021.1985518

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of mean field games in which the optimal strategy of a representative agent depends on the statistical distribution of both the states and controls. We prove some existence results for the forward-backward system of PDEs in a regime never considered so far, where agents may somehow favor a velocity close to the average one. The main step of the proof consists of obtaining a priori estimates on the gradient of the value function by Bernstein's method. Uniqueness is also proved under more restrictive assumptions. Finally, we discuss some examples to which the previously mentioned results apply.

引用

收藏

页码：453 / 488

页数：36

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