{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T07:52:35Z","timestamp":1757577155016},"reference-count":32,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":8625,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1983,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The connection between the minimum\u2010cut problem in a capacitated network and certain combinatorial problems is well\u2010known. This article presents and analyzes a selection problem in the context of a cooperative game, with emphasis on the key role of associated minimum\u2010cut problems. Each coalition selects economic activities from private activities available to its members and public activities available to all coalitions. For each coalition, a minimum\u2010cut problem finds an optimal selection and the value of the characteristic function. The game is a convex game. Applying the Greedy Algorithm involves solving n minimum\u2010cut problems, where <jats:italic>n<\/jats:italic> is the number of players. The solution of <jats:italic>n<\/jats:italic> minimum\u2010cut problem determines whether a proposed payoff vector is in the core. An optimal selection of activities varies monotonically with the coalition membership and with the value of each activity. The Shapley value and each extreme point of the core vary monotonically with the value of each activity.<\/jats:p>","DOI":"10.1002\/net.3230130106","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T14:29:08Z","timestamp":1178893748000},"page":"93-105","source":"Crossref","is-referenced-by-count":11,"title":["Activity selection games and the minimum\u2010cut problem"],"prefix":"10.1002","volume":"13","author":[{"given":"Donald M.","family":"Topkis","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.17.3.230"},{"key":"e_1_2_1_3_2","first-page":"1277","article-title":"Algorithm for solution of a problem of maximum flow in a network with power estimation","volume":"11","author":"Dinic E. A.","year":"1970","journal-title":"Sov. Math. Dokl."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580137"},{"key":"e_1_2_1_5_2","first-page":"69","volume-title":"Combinatorial Structures and Their Applications","author":"Edmonds J.","year":"1970"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/321694.321699"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400875184"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579273"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.13.3.388"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(81)90007-7"},{"key":"e_1_2_1_11_2","unstructured":"E.KalaiandE.Zemel On totally balanced games and games of flow. Discussion Paper No. 413 J. L. Kellogg Graduate School of Management Northwestern University Evanston IL (1980)."},{"key":"e_1_2_1_12_2","first-page":"434","article-title":"Determining the maximal flow in a network by the method of preflows","volume":"15","author":"Karzanov A. V.","year":"1974","journal-title":"Sov. Math. Dokl."},{"key":"e_1_2_1_13_2","first-page":"191","article-title":"A polynomial algorithm in linear programming","volume":"20","author":"Khachian L. G.","year":"1979","journal-title":"Sov. Math. Dokl."},{"key":"e_1_2_1_14_2","first-page":"17","article-title":"Optimum design of open\u2010pit mines","volume":"58","author":"Lerchs H.","year":"1965","journal-title":"Canad. Min. Metall. Bull."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(78)90016-9"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.22.11.1268"},{"key":"e_1_2_1_17_2","unstructured":"J.\u2010C.PicardandM.Queyranne Networks graphs and some nonlinear 0\u20131 programming problems. Technical report EP77\u2013R\u201032 D\u00e9partement de G\u00e9nie Industriel Ecole Polytechnique de Montreal Montreal(1977)."},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.21.1.261"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230050405"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.26.3.422"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100407"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.17.3.200"},{"key":"e_1_2_1_23_2","volume-title":"Annals of Mathematics Studies, Study 28","author":"Shapley L. S.","year":"1953"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800080204"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01753431"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01070506"},{"key":"e_1_2_1_27_2","unstructured":"D. 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