{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T05:24:18Z","timestamp":1751433858106},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p> This paper presents two new results on the enumeration of all extreme equilibria of the sequence form of a two person extensive game. The sequence form of an extensive game is expressed, for the first time to our knowledge, as a parametric linear 0 - 1 program. Considering Ext(P) as the set of all of the sequence form extreme Nash equilibria and Ext(Q) as the set of all the parametric linear 0 - 1 program extreme points, we show that Ext(P) \u2286 Ext(Q). Using exact arithmetics classes, the algorithm E\u03c7MIP Belhaiza (2002); Audet et al. (2006) is extended to enumerate all elements of Ext(Q). A small procedure is then applied in order to obtain all elements of Ext(P). <\/jats:p>","DOI":"10.1142\/s021919890900242x","type":"journal-article","created":{"date-parts":[[2010,4,22]],"date-time":"2010-04-22T07:01:18Z","timestamp":1271919678000},"page":"437-451","source":"Crossref","is-referenced-by-count":9,"title":["A NEW SEQUENCE FORM APPROACH FOR THE ENUMERATION AND REFINEMENT OF ALL EXTREME NASH EQUILIBRIA FOR EXTENSIVE FORM GAMES"],"prefix":"10.1142","volume":"11","author":[{"given":"CHARLES","family":"AUDET","sequence":"first","affiliation":[{"name":"GERAD and D\u00e9partement de math\u00e9matiques et de g\u00e9nie industriel, \u00c9cole Polytechnique de Montr\u00e9al, C.P. 6079, Succ. Centre-ville, Montr\u00e9al (Qu\u00e9bec) Canada H3C 3A7, Canada"}]},{"given":"SLIM","family":"BELHAIZA","sequence":"additional","affiliation":[{"name":"D\u00e9partement de mathmatiques et g\u00e9nie industriel, \u00c9cole Polytechnique de Montr\u00e9al, C.P. 6079, Succ. Centre-ville, Montr\u00e9al (Qu\u00e9bec) Canada H3C 3A7, Canada"}]},{"given":"PIERRE","family":"HANSEN","sequence":"additional","affiliation":[{"name":"GERAD and M\u00e9thodes quantitatives de gestion, HEC Montr\u00e9al, 3000, Chemin de la C\u00f4te-Sainte-Catherine, Montr\u00e9al (Qu\u00e9bec) Canada H3T 2A7, Canada"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-006-9070-3"},{"key":"rf4","volume-title":"Linear Programming","author":"Chv\u00e1tal V.","year":"1998"},{"key":"rf5","unstructured":"G. B.\u00a0Dantzig, Chap. XXI of \"Activity Analysis of Production and Allocation\", ed. T. C.\u00a0Koopmans (John Wiley, New York, 1951)\u00a0pp. 359\u2013373."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2307\/1912320"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0899-8256(92)90035-Q"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01254386"},{"key":"rf9","doi-asserted-by":"crossref","unstructured":"H. W.\u00a0Kuhn, Contributions to the theory of Games II, Annals of Mathematics Studies\u00a028, eds. H. W.\u00a0Kuhn and A.\u00a0Tucker (Princeton Univ. Press, Princeton, 1953)\u00a0pp. 193\u2013216.","DOI":"10.1515\/9781400881970-012"},{"key":"rf10","volume-title":"Game Theory: Analysis of Conflict","author":"Myerson R. B.","year":"1997"},{"key":"rf11","first-page":"678","volume":"3","author":"Romanovskii I. V.","journal-title":"Soviet Mathematics"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0165-4896(88)90040-6"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1006\/game.1996.0050"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00300"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.18.7.448"}],"container-title":["International Game Theory Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021919890900242X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:25:02Z","timestamp":1565169902000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021919890900242X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1142\/S021919890900242X"],"URL":"https:\/\/doi.org\/10.1142\/s021919890900242x","relation":{},"ISSN":["0219-1989","1793-6675"],"issn-type":[{"value":"0219-1989","type":"print"},{"value":"1793-6675","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}