On Weak Solutions to First-Order Discount Mean Field Games

被引：0
作者：
Mitake, Hiroyoshi [1 ]
Terai, Kengo [1 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan
来源：
MINIMAX THEORY AND ITS APPLICATIONS | 2023年 / 8卷 / 01期
关键词：
Mean field games; ergodic problem; vanishing discount approximation; HAMILTON-JACOBI EQUATIONS; REGULARITY; UNIQUENESS; DUALITY; SYSTEMS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish the existence and uniqueness of weak solutions to first-order discount mean field games and a stability result to give the existence for the ergodic problem. We show an example to illustrate the multiplicity of weak solutions to the ergodic problem. With this motivation, we address a selection condition, which is a necessary condition that any limit of solutions under subsequence satisfies. As an application, we show a nontrivial example to get the convergence of weak solutions.
引用
收藏
页码：139 / 170
页数：32
相关论文
共 28 条
[1]  
Cannarsa P., 2004, PROGR NONLINEAR DIFF, V58
[2]   Long Time Average of First Order Mean Field Games and Weak KAM Theory [J].
Cardaliaguet, P. .
DYNAMIC GAMES AND APPLICATIONS, 2013, 3 (04) :473-488
[3]   LONG TIME BEHAVIOR OF THE MASTER EQUATION IN MEAN FIELD GAME THEORY [J].
Cardaliaguet, Pierre ;
Porretta, Alessio .
ANALYSIS & PDE, 2019, 12 (06) :1397-1453
[4]   Weak Solutions for First Order Mean Field Games with Local Coupling [J].
Cardaliaguet, Pierre .
Analysis and Geometry in Control Theory and its Applications, 2015, :111-158
[5]   MEAN FIELD GAMES SYSTEMS OF FIRST ORDER [J].
Cardaliaguet, Pierre ;
Graber, P. Jameson .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2015, 21 (03) :690-722
[6]   Convergence of the solutions of the discounted Hamilton-Jacobi equation [J].
Davini, Andrea ;
Fathi, Albert ;
Iturriaga, Renato ;
Zavidovique, Maxime .
INVENTIONES MATHEMATICAE, 2016, 206 (01) :29-55
[7]   EXISTENCE OF WEAK SOLUTIONS TO STATIONARY MEAN-FIELD GAMES THROUGH VARIATIONAL INEQUALITIES [J].
Ferreira, Rita ;
Gomes, Diogo .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2018, 50 (06) :5969-6006
[8]  
Gilbarg D., 2001, Classics Math., V2nd
[9]   THE SELECTION PROBLEM FOR SOME FIRST-ORDER STATIONARY MEAN-FIELD GAMES [J].
Gomes, Diogo A. ;
Mitake, Hiroyoshi ;
Terai, Kengo .
NETWORKS AND HETEROGENEOUS MEDIA, 2020, 15 (04) :681-710
[10]   One-Dimensional Stationary Mean-Field Games with Local Coupling [J].
Gomes, Diogo A. ;
Nurbekyan, Levon ;
Prazeres, Mariana .
DYNAMIC GAMES AND APPLICATIONS, 2018, 8 (02) :315-351
123