@article{e7875282a4ff4d46b715baf77d56ec0a,
title = "A MAXIMUM PRINCIPLE APPROACH TO A DETERMINISTIC MEAN FIELD GAME OF CONTROL WITH ABSORPTION",
abstract = "We study a deterministic mean field game on finite and infinite time horizons arising in models of optimal exploitation of exhaustible resources. The main characteristic of our game is an absorption constraint on the players' state process. As a result of the state constraint the optimal time of absorption becomes part of the equilibrium. Using Pontryagin's maximum principle, we prove the existence and uniqueness of equilibria and solve the infinite horizon models in closed form. As players may drop out of the game over time, equilibrium production rates need not be monotone nor smooth.",
keywords = "maximum principle, mean field game, optimal exploitation, stochastic control",
author = "Paulwin Graewe and Ulrich Horst and Ronnie Sircar",
note = "Funding Information: ∗Received by the editors April 14, 2021; accepted for publication (in revised form) July 22, 2022; published electronically October 13, 2022. https://doi.org/10.1137/21M1412451 Funding: This work was supported through the profile partnership program between Humboldt-Universit{\"a}t zu Berlin and Princeton University. †Deloitte Consulting GmbH, Kurf{\"u}rstendamm 23, 10719 Berlin, Germany (pgraewe@deloitte.de). ‡Department of Mathematics, and School of Business and Economics, Humboldt-Universit{\"a}t zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (horst@math.hu-berlin.de). §Department of Operations Research and Financial Engineering, Princeton University, Sherrerd Hall, Princeton, NJ 08544 USA (sircar@princeton.edu). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
doi = "10.1137/21M1412451",
language = "English (US)",
volume = "60",
pages = "3173--3190",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",
}