{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:33:30Z","timestamp":1787326410537,"version":"build-2736575974"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"International Research Training Group"},{"name":"DFG CRC\/TRR"},{"name":"Rough Analysis, Stochastic Dynamics and Related Fields"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2025,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We establish a probabilistic framework for analyzing extended mean-field games (MFGs) with multidimensional singular controls and state-dependent jump dynamics and costs. Two key challenges arise when analyzing such games: the state dynamics may not depend continuously on the control, and the reward function may not be u.s.c. Both problems can be overcome by restricting the set of admissible singular controls to controls that can be approximated by continuous ones. We prove that the corresponding set of admissible weak controls is given by the weak solutions to a Marcus-type SDE and provide an explicit characterization of the reward function. The reward function will in general only be u.s.c. To address the lack of continuity, we introduce a novel class of MFGs with a broader set of admissible controls, called MFGs of parametrizations. Parametrizations are laws of state\/control processes that continuously interpolate jumps. We prove that the reward functional is continuous on the set of parametrizations, establish the existence of equilibria in MFGs of parametrizations, and show that the set of Nash equilibria in MFGs of parametrizations and in the underlying MFG with singular controls coincide. This shows that MFGs of parametrizations provide a canonical framework for analyzing MFGs with singular controls and nonlinear jump impact.<\/jats:p>","DOI":"10.1137\/24m1640860","type":"journal-article","created":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T04:00:32Z","timestamp":1745294432000},"page":"1374-1406","source":"Crossref","is-referenced-by-count":1,"title":["Extended Mean-Field Games with Multidimensional Singular Controls and Nonlinear Jump Impact"],"prefix":"10.1137","volume":"63","author":[{"given":"Robert","family":"Denkert","sequence":"first","affiliation":[{"name":"Department of Mathematics, Humboldt University Berlin, 10099 Berlin, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ulrich","family":"Horst","sequence":"additional","affiliation":[{"name":"Department of Mathematics and School of Business and Economics, Humboldt University Berlin, 10099 Berlin, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,4,22]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(99)00102-7"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/20M1377862"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.3934\/jdg.2021012"},{"key":"ref4","volume-title":"Convergence of Probability Measures","author":"Billingsley P.","year":"2013","edition":"2"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1214\/21-AAP1771"},{"key":"ref6","first-page":"1871","volume":"48","author":"Cao H.","year":"2022","journal-title":"Math. 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