@article{daebd180f71f4f578f54428de6eb3d12,
title = "Mean field games with singular controls",
abstract = "This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of cadlag functions.",
keywords = "Mean field game, Relaxed control, Singular control, Skorokhod M1 topology",
author = "Guanxing Fu and Ulrich Horst",
note = "Funding Information: ∗Received by the editors March 31, 2017; accepted for publication (in revised form) September 20, 2017; published electronically November 30, 2017. http://www.siam.org/journals/sicon/55-6/M112374.html Funding: Financial support by the Berlin Mathematical School (BMS) and the SFB 649 Economic Risk is gratefully acknowledged. †Department of Mathematics, and Berlin Mathematical School, Humboldt-Universit{\"a}t zu Berlin Unter den Linden 6, 10099 Berlin, Germany (
[email protected]). ‡Department of Mathematics, and School of Business and Economics, Humboldt-Universit{\"a}t zu Berlin Unter den Linden 6, 10099 Berlin, Germany (
[email protected]). Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",
year = "2017",
month = nov,
day = "30",
doi = "10.1137/17M1123742",
language = "English",
volume = "55",
pages = "3833--3868",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",
}