{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:42:11Z","timestamp":1787319731662,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We study the notion of approachability in a repeated game with vector payoffs from a new point of view using techniques recently developed for qualitative differential games. Namely, we relate the sufficient condition for approachability (B-set) to the notion of discriminating domain for a suitably chosen differential game. The other goal of the present article is to obtain a new precise link between the strategies in the differential game and in the repeated game preserving approachability properties.<\/jats:p>","DOI":"10.1137\/090749098","type":"journal-article","created":{"date-parts":[[2009,7,31]],"date-time":"2009-07-31T18:28:12Z","timestamp":1249064892000},"page":"2461-2479","source":"Crossref","is-referenced-by-count":23,"title":["Repeated Games and Qualitative Differential Games: Approachability and Comparison of Strategies"],"prefix":"10.1137","volume":"48","author":[{"given":"Sami As","family":"Soulaimani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marc","family":"Quincampoix","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sylvain","family":"Sorin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"J.P. Aubin,\n                      Contingent Isaacs equation of a differential game\n                      , in Differential Games and Applications, T. Basar and P. Bernhard, eds., Lecture Notes in Control and Inform. Sci. 119, Springer, Berlin, 1989, pp. 51\u201361.","DOI":"10.1007\/BFb0004262"},{"key":"R2","unstructured":"J.P. Aubin,\n                      Viability Theory\n                      , Birkh\u00e4user, Boston, 1991."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"J.P. Aubin and A. Cellina,\n                      Differential Inclusions: Set-Valued Maps and Viability Theory\n                      , Springer, Berlin, 1984.","DOI":"10.1007\/978-3-642-69512-4"},{"key":"R4","unstructured":"J.P. Aubin and H. Frankowska,\n                      Set-Valued Analysis\n                      , Birkh\u00e4user, Boston, 1990."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012904439301"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1060.0213"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1956.6.1"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.11.076"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.5802\/aif.319"},{"key":"R10","unstructured":"P. Cardaliaguet,\n                      Domaines Discriminants en Jeux Diff\u00e9rentiels\n                      , Th\u00e8se de doctorat, Universit\u00e9 Paris IX-Dauphine, Paris, 1994."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S036301299427223X"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900057"},{"key":"R13","unstructured":"P. Cardaliaguet,\n                      Nonzero-Sum Differential Games Revisited\n                      , Working paper, 1997 (unpublished)."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1994280404411"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"P. Cardaliaguet, M. Quincampoix, and P. Saint-Pierre,\n                      Differential games through viability theory: Old and recent results\n                      , in Advances in Dynamic Games Theory, Ann. Internat. Soc. Dynam. Games, S. Jorgensen, M. Quincampoix, and T. Vincent, eds., Birkh\u00e4user, Boston, 2007, pp. 3\u201336.","DOI":"10.1007\/978-0-8176-4553-3_1"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"N. Cesa-Bianchi and G. Lugosi,\n                      Prediction, Learning, and Games\n                      , Cambridge University Press, Cambridge, UK, 2006.","DOI":"10.1017\/CBO9780511546921"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(72)90022-8"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1006\/game.1999.0740"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2005.00625.x"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693422"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"N. N. Krasovskii and A. I. Subbotin,\n                      Game-Theoretical Control Problems\n                      , Springer, New York, 1988.","DOI":"10.1007\/978-1-4612-3716-7"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/s001820200115"},{"key":"R23","unstructured":"E. Lehrer and E. Solan,\n                      No-Regret with Bounded Computational Capacity\n                      , manuscript, 2003."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1060.0211"},{"key":"R25","first-page":"551","volume":"24","author":"Nagumo M.","year":"1942","journal-title":"Proc. Phys.-Math. Soc. Japan (3)"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"R. T. Rockafellar and R. J.B. Wets,\n                      Variational Analysis\n                      , Springer, Berlin, 1998.","DOI":"10.1007\/978-3-642-02431-3"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/BF00929440"},{"key":"R28","unstructured":"S. Sorin,\n                      A First Course on Zero-Sum Repeated Games\n                      , Math. Appl. (Berlin) 37, Springer, Berlin, 2002."},{"key":"R29","unstructured":"X. Spinat,\n                      Approchabilit\u00e9 et Jeux Diff\u00e9rentiels\n                      , Th\u00e8se de doctorat, Universit\u00e9 Paris X-Nanterre, Paris, 2000."},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1287\/moor.27.1.31.333"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1137\/0305009"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1287\/moor.17.4.781"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090749098","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:51:53Z","timestamp":1787316713000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090749098"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/090749098"],"URL":"https:\/\/doi.org\/10.1137\/090749098","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}