Long-Time Behavior of First-Order Mean Field Games on Euclidean Space

被引：10

作者：

Cannarsa, Piermarco ^{[1
]}

Cheng, Wei ^{[2
]}

Mendico, Cristian ^{[1
]}

Wang, Kaizhi ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, Rome, Italy

[2] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[3] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

DYNAMIC GAMES AND APPLICATIONS | 2020年 / 10卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Mean field games; Weak KAM theory; Long-time behavior; Viscosity solutions; WEAK KAM THEOREM;

D O I：

10.1007/s13235-019-00321-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to study the long-time behavior of solutions to deterministic mean field games systems on Euclidean space. This problem was addressed on the torus Tnin Cardaliaguet (Dyn Games Appl 3:473-488, 2013), where solutions are shown to converge to the solution of a certain ergodic mean field games system on Tn By adapting the approach in Fathi and Maderna (Nonlinear Differ Equ Appl NoDEA 14:1-27, 2007), we identify structural conditions on the Lagrangian, under which the corresponding ergodic system can be solved in Rn Then, we show that time-dependent solutions converge to the solution of such a stationary system on all compact subsets of the whole space.

引用

页码：361 / 390

页数：30

共 23 条

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