Deterministic Limit of Mean Field Games Associated with Nonlinear Markov Processes

被引:2
|
作者
Averboukh, Yurii [1 ,2 ]
机构
[1] Krasovskii Intitute Math & Mech UrB RAS, 16 S Kovalevskaya, Ekaterinburg, Russia
[2] Ural Fed Univ, 19 Mira, Ekaterinburg, Russia
来源
APPLIED MATHEMATICS AND OPTIMIZATION | 2020年 / 81卷 / 03期
关键词
Mean field games; Deterministic limit; Minimax solutions;
D O I
10.1007/s00245-018-9486-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The paper is concerned with the deterministic limit of mean field games with a nonlocal coupling. It is assumed that the dynamics of mean field games are given by nonlinear Markov processes. This type of games includes stochastic mean field games as well as mean field games with finite state space. We consider the limiting deterministic mean field game within the framework of minimax approach. The concept of minimax solutions is close to the probabilistic formulation. In this case the Hamilton-Jacobi equation is considered in the minimax/viscosity sense, whereas the flow of probabilities is determined by the probability on the set of solutions of the differential inclusion associated with the Hamilton-Jacobi equation such that those solutions are viable in the graph of the minimax solution. The main result of the paper is the convergence (up to subsequence) of the solutions of the mean field games to the minimax solution of a deterministic mean field game in the case when the underlying dynamics converge to the deterministic evolution.
引用
收藏
页码:711 / 738
页数:28
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