A Discrete Weak KAM Method for First-Order Stationary Mean Field Games

被引：2

作者：

Iturriaga, Renato ^{[1
]}

Wang, Kaizhi ^{[2
]}

机构：

[1] Ctr Invest Matemat, Guanajuato, Mexico

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

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2023年 / 22卷 / 02期

基金：

中国国家自然科学基金; 上海市自然科学基金;

关键词：

mean field games; Mather theory; discretization; weak KAM theory; discretization problem; APPROXIMATION; CONVERGENCE; SCHEME;

D O I：

10.1137/22M1508212

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a discrete weak KAM method for finding solutions of a class of first-order stationary mean field games systems. Especially, such solutions have clear dynamical meaning. First, we dis-cretize Lax-Oleinik equations by discretizing in time, and then we prove the existence of minimizing holonomic measures for mean field games. We obtain two sequences of solutions {ui\} of discrete Lax-Oleinik equations and minimizing holonomic measures {mi\} for mean field games and show that (ui, mi) converges to a solution of the stationary mean field games systems. Finally, we briefly describe how to implement a discretization in the space variable also.

引用

页码：1253 / 1274

页数：22

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