
Regularity Theory for Mean-Field Game Systems
Springer (Publisher)
Published in October 2016
Book
Paperback/Softback
XIV, 156 pages
978-3-319-38932-5 (ISBN)
Description
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Reviews / Votes
"This book is concerned with mean field game systems, or MFG systems for short. Such systems describe an infinite number of rational agents in competition. ... The book is an accesible introduction to MFG systems, readable by anyone with a basic knowledge of partial differential equations." (Teemu Lukkari, Mathematical Reviews, October, 2017)More details
Product info
Book
Series
Edition
1st ed. 2016
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
College/higher education
Illustrations
4
4 farbige Abbildungen
XIV, 156 p. 4 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 10 mm
Weight
271 gr
ISBN-13
978-3-319-38932-5 (9783319389325)
DOI
10.1007/978-3-319-38934-9
Schweitzer Classification
Other editions
Additional editions

Diogo A. Gomes | Edgard A. Pimentel | Vardan Voskanyan
Regularity Theory for Mean-Field Game Systems
E-Book
09/2016
Springer
€64.19
Available for download
Content
Preface.- Introduction.- Explicit solutions, special transformations, and further examples.- Estimates for the Hamilton-Jacobi equation.- Estimates for the Transport and Fokker-Planck equations.- The nonlinear adjoint method.- Estimates for MFGs.- A priori bounds for stationary models.- A priori bounds for time-dependent models.- A priori bounds for models with singularities.- Non-local mean-field games - existence.- Local mean-field games - existence.- References.- Index.