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We show that when the singular perturbations parameter tends to zero, the upper (lower) value function of the dynamic game has a limit which coincides with a viscosity solution of a Hamilton--Jacobi--Isaacs-type equation. Two examples are given to demonstrate the potential of the proposed technique.<\/jats:p>","DOI":"10.1137\/s036301290037908x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"826-850","source":"Crossref","is-referenced-by-count":12,"title":["Limit Hamilton--Jacobi--Isaacs Equations for Singularly Perturbed Zero-Sum Dynamic (Discrete Time) Games"],"prefix":"10.1137","volume":"41","author":[{"given":"Peng","family":"Shi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S036301299528458X"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500022903"},{"key":"R3","volume-title":"Viability theory","author":"Aubin Jean\u2010Pierre","year":"1991"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/9.633828"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1984.33.33040"},{"key":"R6","volume-title":"Controlled Markov processes and viscosity solutions","author":"Fleming Wendell","year":"1993"},{"key":"R7","volume-title":"Differential games","author":"Friedman Avner","year":"1971"},{"key":"R8","first-page":"0","volume":"22","author":"Ga tsgori V.","year":"1986","journal-title":"Differentsial rime nye Uravneniya"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0330065"},{"key":"R10","unstructured":"V.Gai\u02d8tsgori, Upravlenie sistemami s bystrymi i medlennymi dvizheniyami, \u201cNauka\u201d, 1991, 224\u20130, With an English summary93f:49001"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1109\/9.222301"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1996.0352"},{"key":"R13","unstructured":"V. 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