The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Interfaces and Free Boundaries

Full-Text PDF (181 KB) | Metadata | Table of Contents | IFB summary
Volume 17, Issue 1, 2015, pp. 55–68
DOI: 10.4171/IFB/333

Published online: 2015-05-26

Obstacle mean-field game problem

Diogo A. Gomes[1] and Stefania Patrizi[2]

(1) King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
(2) Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions.

Keywords: Mean-field games, obstacle problem, penalization method

Gomes Diogo, Patrizi Stefania: Obstacle mean-field game problem. Interfaces Free Bound. 17 (2015), 55-68. doi: 10.4171/IFB/333