{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:58Z","timestamp":1787323258076,"version":"build-2736575974"},"reference-count":19,"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":[[2002,1]]},"abstract":"<jats:p>Let (X,Y,Z) be a triple of payoff processes defining a Dynkin game \\tilde R(\\sigma,\\tau) &amp;=&amp; E\\left[ X_\\sigma\\1_{\\{\\tau &gt; \\sigma\\}} +Y_\\tau \\1_{\\{\\tau &lt; \\sigma\\}} +Z_\\tau \\1_{\\{\\tau=\\sigma\\}}\\right] , where $\\sigma$ and $\\tau$ are stopping times valued in [0,T]. In the case Z=Y, it is well known that the condition X $\\leq$ Y is needed in order to establish the existence of value for the game, i.e., $\\inf_{\\tau}\\sup_{\\sigma}\\tilde R(\\sigma,\\tau)$ $=$ $\\sup_{\\sigma}\\inf_{\\tau}\\tilde R(\\sigma,\\tau)$.<\/jats:p>\n                  <jats:p>In order to remove the condition X $\\leq$ Y, we introduce an extension of the Dynkin game by allowing for an extended set of strategies, namely, the set of mixed strategies. The main result of the paper is that the extended Dynkin game has a value when $Z\\leq Y$, and the processes X and Y are restricted to be semimartingales continuous at the terminal time T.<\/jats:p>","DOI":"10.1137\/s0363012900369812","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1073-1088","source":"Crossref","is-referenced-by-count":84,"title":["Continuous-Time Dynkin Games with Mixed Strategies"],"prefix":"10.1137","volume":"41","author":[{"given":"Nizar","family":"Touzi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Vieille","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"M. Alario\u2010Nazaret, J.\u2010P. Lepeltier, B. Marchal, Dynkin games, Lecture Notes in Control and Inform. Sci., Vol. 43, Springer, Berlin, 1982, 23\u20133287b:90159","DOI":"10.1007\/BFb0044285"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Robert Aumann, Mixed and behavior strategies in infinite extensive games, Princeton Univ. Press, Princeton, N.J., 1964, 627\u201365031:1116","DOI":"10.1515\/9781400882014-029"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(74)90076-7"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01844871"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994889"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1041903216"},{"key":"R7","volume-title":"Probabilit\u00e9s et potentiel","author":"Dellacherie Claude","year":"1975"},{"key":"R8","first-page":"16","volume":"185","author":"Dynkin E.","year":"1969","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"E. B. Dynkin and A. A. Yushkevich (1968),\n                      Theorems and Problems in Markov Processes\n                      , Plenum Press, New York.","DOI":"10.1007\/978-1-4899-5591-3"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02514-7"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/b98840"},{"key":"R12","unstructured":"I. Karatzas and H. Wang (2001),\n                      Connections between bounded variation control and Dynkin games\n                      , in Optimal Control and Partial Differential Equations (Volume in honor of A. Bensoussan), J. L. Menaldi, E. Rofman, and A. Sulem, eds., IOS Press, Amsterdam, pp. 363\u2013373."},{"key":"R13","doi-asserted-by":"crossref","unstructured":"H. Kuhn, Extensive games and the problem of information, Annals of Mathematics Studies, no. 28, Princeton University Press, Princeton, N. 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