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The associated quasi-variational-inequalities include an essential game component regarding the interactions among players, which may be interpreted as the analytical representation of the conditional optimality for NEs. The derivation of NEs involves solving first a multidimensional free boundary problem and then a Skorokhod problem. Finally, we present an intriguing connection between these NE strategies and controlled rank-dependent stochastic differential equations.<\/jats:p>","DOI":"10.1137\/20m1322558","type":"journal-article","created":{"date-parts":[[2022,3,17]],"date-time":"2022-03-17T11:35:15Z","timestamp":1647516915000},"page":"758-785","source":"Crossref","is-referenced-by-count":6,"title":["A Class of Stochastic Games and Moving Free Boundary Problems"],"prefix":"10.1137","volume":"60","author":[{"given":"Xin","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7228-1954","authenticated-orcid":true,"given":"Wenpin","family":"Tang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4293-3450","authenticated-orcid":true,"given":"Renyuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,3,17]]},"reference":[{"key":"atypb1","unstructured":"D. Aldous,\n                      \"Up the River\" Game Story\n                      , 2002,http:\/\/www.stat.berkeley.edu\/ aldous\/Research\/OP\/river.pdf."},{"key":"atypb2","unstructured":"L. Arnold,\n                      Stochastic Differential Equations: Theory and Applications\n                      , Wiley, New York, 1974."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1214\/009117906000000359"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1214\/105051605000000449"},{"key":"atypb5","unstructured":"M. Basei, H. Cao, and X. 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Bosman,\n                      Bounded-Velocity Stochastic Control for Dynamic Resource Allocation\n                      , preprint,arXiv:1801.01221, 2018."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1561\/1300000001"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2006.04.008"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-010-0336-z"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/17M1159531"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2014.06.011"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP986"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.4310\/CIS.2006.v6.n3.a5"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP706"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1214\/105051606000000899"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.2307\/1426435"},{"key":"atypb25","first-page":"105","author":"Karatzas I.","year":"2012","journal-title":"NJ"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/BF01158808"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2014.0700"},{"key":"atypb28","unstructured":"H. D. Kwon,\n                      Game of variable contributions to the common good under uncertainty\n                      , preprint, Oper. Res., 2020."},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.09.019"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.09.018"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1007\/s11537-007-0657-8"},{"key":"atypb32","first-page":"247","author":"Levy R.","year":"2003","journal-title":"New York"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2007.10.013"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012903423715"},{"key":"atypb35","first-page":"291","author":"Meyer P. A.","year":"1976","journal-title":"New York"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1109\/TSG.2012.2203341"},{"key":"atypb37","first-page":"265","volume":"16","author":"Shreve S. E.","year":"1991","journal-title":"Appl. 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