Existence of a solution to an equation arising from the theory of Mean Field Games

被引：61

作者：

Gangbo, Wilfrid ^{[1
]}

Swiech, Andrzej ^{[1
]}

机构：

[1] Georgia Inst Technol, Atlanta, GA 30332 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 11期

基金：

美国国家科学基金会;

关键词：

NASH; PRINCIPLE; SYSTEMS;

D O I：

10.1016/j.jde.2015.08.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a small time strong solution to a nonlocal Hamilton Jacobi equation (1.1) introduced in [481, the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton Jacobi equations studied in [2,19,20] and solutions to (1. 1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in 148], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2). (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：6573 / 6643

页数：71

共 52 条

[1] Transport equation and Cauchy problem for BV vector fields
Ambrosio, L
[J]. INVENTIONES MATHEMATICAE, 2004, 158 (02) : 227 - 260
[2] Ambrosio L., 2005, Gradient Flows: in Metric Spaces and in the Space of Probability Measures
[3] Hamiltonian ODEs in the wasserstein space of probability measures
Ambrosio, Luigi
Gangbo, Wilfred
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2008, 61 (01) : 18 - 53
[4] On a class of first order Hamilton-Jacobi equations in metric spaces
Ambrosio, Luigi
Feng, Jin
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (07) : 2194 - 2245
[5] [Anonymous], [No title captured]
[6] Aumann R. J., 1974, The Shapley value
[7] MARKETS WITH A CONTINUUM OF TRADERS
AUMANN, RJ
[J]. ECONOMETRICA, 1964, 32 (1-2) : 39 - 50
[8] Balandat M, 2013, P AMER CONTR CONF, P2527
[9] Bensoussan A, 2013, SPRINGERBRIEF MATH, P1, DOI 10.1007/978-1-4614-8508-7
[10] The Master equation in mean field theory
Bensoussan, Alain
Frehse, Jens
Yam, Sheung Chi Phillip
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2015, 103 (06): : 1441 - 1474

← 1 2 3 4 5 6 →