{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T09:12:22Z","timestamp":1721034742571},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,3,28]],"date-time":"2023-03-28T00:00:00Z","timestamp":1679961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Istituto Nazionale di Alta Matematica, Italy"},{"name":"Department of Math- ematics, University of Roma Tor Vergata","award":["E83C23000330006"],"award-info":[{"award-number":["E83C23000330006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,6,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash equilibrium in mixed strategies exists and it is a Mather measure for the Lagrangian system defined by the cost functional. In conclusion, we show that the mean field limit of the N-players game is described by the ergodic partial differential equation\u2019s system for a continuum of players.<\/jats:p>","DOI":"10.1093\/imamci\/dnad006","type":"journal-article","created":{"date-parts":[[2023,3,29]],"date-time":"2023-03-29T01:33:48Z","timestamp":1680053628000},"page":"192-209","source":"Crossref","is-referenced-by-count":1,"title":["Differential N-players game: Nash equilibria and Mather measures"],"prefix":"10.1093","volume":"40","author":[{"given":"Cristian","family":"Mendico","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Rome Tor Vergata , Via della Ricerca Scientifica 1, 00133 Roma , Italy"}]}],"member":"286","published-online":{"date-parts":[[2023,3,28]]},"reference":[{"key":"2023061612573323400_ref1","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/s00030-016-0397-7","article-title":"Nonlinear elliptic systems and mean-field games. 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