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：
上海市自然科学基金; 中国国家自然科学基金;
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
收藏
页码：1253 / 1274
页数：22
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