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We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called fictitious play, and this without any further potential or monotone structure. Several numerical examples are provided to support our theoretical analysis. <\/jats:p><jats:p> Funding: F. Delarue acknowledges the financial support of the European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation programme [AdG ELISA project, Grant 101054746]. A. Vasileiadis acknowledge the financial support of French ANR project ANR-19-P3IA-0002-3IA C\u00f4te d'Azur-Nice-Interdisciplinary Institute for Artificial Intelligence. <\/jats:p>","DOI":"10.1287\/moor.2021.0157","type":"journal-article","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T10:16:48Z","timestamp":1721816208000},"page":"1762-1831","source":"Crossref","is-referenced-by-count":0,"title":["Exploration Noise for Learning Linear-Quadratic Mean Field Games"],"prefix":"10.1287","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5511-1088","authenticated-orcid":false,"given":"Fran\u00e7ois","family":"Delarue","sequence":"first","affiliation":[{"name":"CNRS, LJAD, Universit\u00e9 C\u00f4te d\u2019Azur, 06108 Nice Cedex 2, France"}]},{"given":"Athanasios","family":"Vasileiadis","sequence":"additional","affiliation":[{"name":"CNRS, LJAD, Universit\u00e9 C\u00f4te d\u2019Azur, 06108 Nice Cedex 2, France"}]}],"member":"109","reference":[{"doi-asserted-by":"publisher","key":"B1","DOI":"10.1137\/090758477"},{"doi-asserted-by":"publisher","key":"B2","DOI":"10.1007\/s00245-016-9391-z"},{"key":"B3","first-page":"203","volume-title":"Mean Field Games, Cetraro, Italy 2019","author":"Achdou Y","year":"2021"},{"doi-asserted-by":"publisher","key":"B4","DOI":"10.1137\/100790069"},{"doi-asserted-by":"publisher","key":"B5","DOI":"10.1137\/120882421"},{"doi-asserted-by":"publisher","key":"B6","DOI":"10.1007\/s10957-019-01619-3"},{"doi-asserted-by":"publisher","key":"B7","DOI":"10.1016\/j.matpur.2021.01.003"},{"doi-asserted-by":"publisher","key":"B8","DOI":"10.1007\/s00332-018-9525-3"},{"doi-asserted-by":"publisher","key":"B9","DOI":"10.1007\/s10957-015-0725-9"},{"doi-asserted-by":"publisher","key":"B10","DOI":"10.1214\/07-AAP448"},{"doi-asserted-by":"publisher","key":"B11","DOI":"10.1214\/13-AAP943"},{"doi-asserted-by":"publisher","key":"B12","DOI":"10.1137\/16M1095615"},{"doi-asserted-by":"publisher","key":"B14","DOI":"10.1051\/cocv\/2016004"},{"doi-asserted-by":"publisher","key":"B15","DOI":"10.1137\/120902987"},{"doi-asserted-by":"publisher","key":"B16","DOI":"10.3934\/dcds.2015.35.4269"},{"doi-asserted-by":"publisher","key":"B17","DOI":"10.1007\/978-3-319-58920-6_1"},{"doi-asserted-by":"publisher","key":"B18","DOI":"10.1007\/978-3-319-56436-4"},{"doi-asserted-by":"publisher","key":"B19","DOI":"10.1214\/14-AAP1020"},{"doi-asserted-by":"publisher","key":"B20","DOI":"10.1137\/19M1274377"},{"doi-asserted-by":"publisher","key":"B21","DOI":"10.1214\/21-AAP1715"},{"doi-asserted-by":"publisher","key":"B24","DOI":"10.1080\/03605302.2021.1955256"},{"doi-asserted-by":"publisher","key":"B25","DOI":"10.1214\/18-AAP1429"},{"doi-asserted-by":"publisher","key":"B26","DOI":"10.1016\/j.spa.2014.11.018"},{"doi-asserted-by":"publisher","key":"B27","DOI":"10.1214\/18-AAP1407"},{"doi-asserted-by":"publisher","key":"B28","DOI":"10.1214\/EJP.v10-295"},{"doi-asserted-by":"publisher","key":"B29","DOI":"10.1016\/S0304-4149(02)00085-6"},{"doi-asserted-by":"publisher","key":"B30","DOI":"10.1007\/978-3-540-40004-2_12"},{"doi-asserted-by":"publisher","key":"B31","DOI":"10.1007\/s40072-019-00135-9"},{"doi-asserted-by":"publisher","key":"B32","DOI":"10.1016\/j.spa.2019.04.005"},{"doi-asserted-by":"publisher","key":"B33","DOI":"10.1214\/105051605000000674"},{"doi-asserted-by":"publisher","key":"B35","DOI":"10.1109\/TAC.1971.1099832"},{"doi-asserted-by":"publisher","key":"B36","DOI":"10.1162\/089976600300015961"},{"doi-asserted-by":"publisher","key":"B37","DOI":"10.1007\/s40304-017-0117-6"},{"doi-asserted-by":"publisher","key":"B38","DOI":"10.1609\/aaai.v34i05.6203"},{"doi-asserted-by":"publisher","key":"B39","DOI":"10.1016\/j.automatica.2022.110177"},{"doi-asserted-by":"publisher","key":"B40","DOI":"10.1007\/s13235-016-0200-8"},{"doi-asserted-by":"publisher","key":"B42","DOI":"10.1214\/105051605000000412"},{"doi-asserted-by":"publisher","key":"B45","DOI":"10.1016\/j.matpur.2019.02.006"},{"key":"B46","first-page":"56","volume":"24","author":"Hambly B","year":"2023","journal-title":"J. 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