{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:36:33Z","timestamp":1787319393883,"version":"3.56.0"},"reference-count":6,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100015023","name":"LABEX ECODEC","doi-asserted-by":"crossref","award":["ANR-11-IDEX-0003"],"award-info":[{"award-number":["ANR-11-IDEX-0003"]}],"id":[{"id":"10.13039\/501100015023","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100015023","name":"LABEX ECODEC","doi-asserted-by":"crossref","award":["ANR-11-LABX-0047"],"award-info":[{"award-number":["ANR-11-LABX-0047"]}],"id":[{"id":"10.13039\/501100015023","id-type":"DOI","asserted-by":"crossref"}]},{"name":"FIME Research Initiative"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game. We place ourselves in the framework of relaxed optimal stopping, which amounts to looking for the optimal occupation measure of the stopper rather than the optimal stopping time. This framework allows us to prove the existence of a relaxed Nash equilibrium and the uniqueness of the associated value of the representative agent under mild assumptions. Further, we prove a rigorous relation between relaxed Nash equilibria and the notion of mixed solutions introduced in earlier works on the subject and provide a criterion under which the optimal strategies are pure strategies, that is, behave in a similar way to stopping times. Finally, we present a numerical method for computing the equilibrium in the case of potential games and show its convergence.<\/jats:p>","DOI":"10.1137\/18m1233480","type":"journal-article","created":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T14:25:26Z","timestamp":1594045526000},"page":"1795-1821","source":"Crossref","is-referenced-by-count":33,"title":["Mean-Field Games of Optimal Stopping: A Relaxed Solution Approach"],"prefix":"10.1137","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1980-7272","authenticated-orcid":true,"given":"G\u00e9raldine","family":"Bouveret","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roxana","family":"Dumitrescu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Tankov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,7,6]]},"reference":[{"key":"atypb14","doi-asserted-by":"crossref","unstructured":",\n                      Linear programming formulation for optimal stopping problems\n                      , SIAM J. Control Optim., 40, pp. 1965-1982.","DOI":"10.1137\/S0363012900377663"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"(1987)},\n                      Compactification methods in the control of degenerate diffusions: Existence of an optimal control\n                      , Stochastics, 20, pp. 169-219.","DOI":"10.1080\/17442508708833443"},{"key":"atypb18","unstructured":",\n                      Stochastic differential equations and applications\n                      , Vol. 1, Probab. Math. Stat. 28, Academic Press, New York, 1975."},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"(2006)},\n                      Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle\n                      , Commun. Inf. Syst., 6, pp. 221-252.","DOI":"10.4310\/CIS.2006.v6.n3.a5"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":",\n                      Mean field games via controlled martingale problems: Existence of Markovian equilibria\n                      , Stochastic Process. Appl., 125, pp. 2856-2894.","DOI":"10.1016\/j.spa.2015.02.006"},{"key":"atypb32","first-page":"48","volume":"2","author":"Measures","year":"1965","journal-title":"Amer. Math. Soc. Ser."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1233480","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:46:32Z","timestamp":1787316392000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1233480"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/18M1233480"],"URL":"https:\/\/doi.org\/10.1137\/18m1233480","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}