{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T06:45:07Z","timestamp":1777617907770,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,1,19]],"date-time":"2017-01-19T00:00:00Z","timestamp":1484784000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Netherlands Organization for Scientific Research","award":["NWO grant 400-08-026"],"award-info":[{"award-number":["NWO grant 400-08-026"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1007\/s10957-016-1057-0","type":"journal-article","created":{"date-parts":[[2017,1,20]],"date-time":"2017-01-20T00:29:14Z","timestamp":1484872154000},"page":"1008-1022","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Power Measures and Solutions for Games Under Precedence Constraints"],"prefix":"10.1007","volume":"172","author":[{"given":"Encarnaci\u00f3n","family":"Algaba","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ren\u00e9","family":"van den Brink","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris","family":"Dietz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,1,19]]},"reference":[{"key":"1057_CR1","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1287\/moor.2.3.225","volume":"2","author":"RB Myerson","year":"1977","unstructured":"Myerson, R.B.: Graphs and cooperation in games. Math. Oper. Res. 2, 225\u2013229 (1977)","journal-title":"Math. Oper. Res."},{"key":"1057_CR2","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF01253782","volume":"20","author":"RP Gilles","year":"1992","unstructured":"Gilles, R.P., Owen, G., van den Brink, R.: Games with permission structures: the conjunctive approach. Int. J. Game Theory 20, 277\u2013293 (1992)","journal-title":"Int. J. Game Theory"},{"key":"1057_CR3","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF01258278","volume":"21","author":"U Faigle","year":"1992","unstructured":"Faigle, U., Kern, W.: The Shapley value for cooperative games under precedence constraints. Int. J. Game Theory 21, 249\u2013266 (1992)","journal-title":"Int. J. Game Theory"},{"key":"1057_CR4","first-page":"1","volume":"282","author":"E Algaba","year":"2004","unstructured":"Algaba, E., Bilbao, M., van den Brink, R., Jim\u00e9nez-Losada, A.: Cooperative games on antimatroids. Math. Methods Oper. Res. 282, 1\u201315 (2004)","journal-title":"Math. Methods Oper. Res."},{"key":"1057_CR5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0166-218X(99)00218-8","volume":"103","author":"JM Bilbao","year":"2000","unstructured":"Bilbao, J.M., Edelman, P.H.: The Shapley value on convex geometries. Discrete Appl. Math. 103, 33\u201340 (2000)","journal-title":"Discrete Appl. Math."},{"key":"1057_CR6","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1137\/S0895480102402745","volume":"17","author":"JM Bilbao","year":"2003","unstructured":"Bilbao, J.M.: Cooperative games under augmenting systems. SIAM J. Discrete Math. 17, 122\u2013133 (2003)","journal-title":"SIAM J. Discrete Math."},{"key":"1057_CR7","doi-asserted-by":"crossref","first-page":"3472","DOI":"10.1016\/j.ins.2006.02.011","volume":"176","author":"A Honda","year":"2006","unstructured":"Honda, A., Grabisch, M.: Entropy of capacities on lattices and set systems. Inf. Sci. 176, 3472\u20133489 (2006)","journal-title":"Inf. Sci."},{"key":"1057_CR8","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.mathsocsci.2009.07.003","volume":"58","author":"F Lange","year":"2009","unstructured":"Lange, F., Grabisch, M.: Values on regular games under Kirchhoff\u2019s laws. Math. Soc. Sci. 58, 322\u2013340 (2009)","journal-title":"Math. Soc. Sci."},{"key":"1057_CR9","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s001860000060","volume":"52","author":"E Algaba","year":"2000","unstructured":"Algaba, E., Bilbao, M., Borm, P., L\u00f3pez, J.: The position value for union stable systems. Math. Methods Oper. Res. 52, 221\u2013236 (2000)","journal-title":"Math. Methods Oper. Res."},{"key":"1057_CR10","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s001860100159","volume":"54","author":"E Algaba","year":"2001","unstructured":"Algaba, E., Bilbao, M., Borm, P., L\u00f3pez, J.: The Myerson value for union stable structures. Math. Methods Oper. Res. 54, 359\u2013371 (2001)","journal-title":"Math. Methods Oper. Res."},{"key":"1057_CR11","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s10479-012-1228-9","volume":"201","author":"M Grabisch","year":"2012","unstructured":"Grabisch, M., Sudh\u00f6lter, P.: The bounded core for games with precedence constraints. Ann. Oper. Res. 201, 251\u2013264 (2012)","journal-title":"Ann. Oper. Res."},{"key":"1057_CR12","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/s00182-015-0465-y","volume":"45","author":"M Grabisch","year":"2016","unstructured":"Grabisch, M., Sudh\u00f6lter, P.: Characterizations of solutions for games with precedence constraints. Int. J. Game Theory 45, 269\u2013290 (2016)","journal-title":"Int. J. Game Theory"},{"key":"1057_CR13","volume-title":"The Algorithm Design Manual","author":"SS Skiena","year":"2010","unstructured":"Skiena, S.S.: The Algorithm Design Manual, 2nd edn. Springer, Berlin (2010)","edition":"2"},{"key":"1057_CR14","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1007\/s11750-015-0380-1","volume":"24","author":"MG Fiestras-Janeiro","year":"2016","unstructured":"Fiestras-Janeiro, M.G., S\u00e1nchez-Rodr\u00edguez, E., Schuster, M.: A precedence constraint value revisited. TOP. 24, 156\u2013170 (2016)","journal-title":"TOP."},{"key":"1057_CR15","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0378-8733(87)90023-2","volume":"9","author":"RV Gould","year":"1987","unstructured":"Gould, R.V.: Measures of betweenness in non-symmetric networks. Soc. Netw. 9, 277\u2013282 (1987)","journal-title":"Soc. Netw."},{"key":"1057_CR16","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/0378-8733(94)90015-9","volume":"16","author":"DR White","year":"1994","unstructured":"White, D.R., Borgatti, S.P.: Betweenness centrality measures for directed graphs. Soc. Netw. 16, 335\u2013346 (1994)","journal-title":"Soc. Netw."},{"key":"1057_CR17","first-page":"1141","volume":"22","author":"R Brink","year":"2000","unstructured":"Brink, R., van den, R., Gilles, R.P.: Measuring domination in directed networks. Soc. Netw. 22, 1141\u20131157 (2000)","journal-title":"Soc. Netw."},{"key":"1057_CR18","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1023\/A:1024162419357","volume":"53","author":"R Brink van den","year":"2002","unstructured":"van den Brink, R., Borm, P.: Digraph competitions and cooperative games. Theory Decis. 53, 327\u2013342 (2002)","journal-title":"Theory Decis."},{"key":"1057_CR19","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1016339832755","volume":"109","author":"P Borm","year":"2002","unstructured":"Borm, P., van den Brink, R., Slikker, M.: An iterative procedure for evaluating digraph competitions. Ann. Oper. Res. 109, 61\u201375 (2002)","journal-title":"Ann. Oper. Res."},{"key":"1057_CR20","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s00355-003-0308-9","volume":"24","author":"PJJ Herings","year":"2005","unstructured":"Herings, P.J.J., van der Laan, G., Talman, A.J.J.: The positional power of nodes in digraphs. Soc. Choice Welf. 24, 439\u2013454 (2005)","journal-title":"Soc. Choice Welf."},{"key":"1057_CR21","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.socnet.2011.04.001","volume":"33","author":"M Pozo del","year":"2011","unstructured":"del Pozo, M., Manuel, C., Gonz\u00e1lez-Arang\u00fcena, E., Owen, G.: Centrality in directed social networks. A game theoretic approach. Soc. Netw. 33, 191\u2013200 (2011)","journal-title":"Soc. Netw."},{"key":"1057_CR22","first-page":"325","volume-title":"Contributions to the Theory of Games IV","author":"JC Harsanyi","year":"1959","unstructured":"Harsanyi, J.C.: A bargaining model for cooperative $$n$$ n -person games. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games IV, pp. 325\u2013355. Princeton University Press, Princeton (1959)"},{"key":"1057_CR23","first-page":"307","volume-title":"Contributions to the Theory of Games","author":"LS Shapley","year":"1953","unstructured":"Shapley, L.S.: A value for $$n$$ n -person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, vol. 2, pp. 307\u2013317. Princeton University Press, Princeton (1953)"},{"key":"1057_CR24","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s001860200250","volume":"57","author":"E Algaba","year":"2003","unstructured":"Algaba, E., Bilbao, M., van den Brink, R., Jim\u00e9nez-Losada, A.: Axiomatizations of the Shapley value for games on antimatroids. Math. Methods Oper. Res. 57, 49\u201365 (2003)","journal-title":"Math. Methods Oper. Res."},{"key":"1057_CR25","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1016\/j.ejor.2008.04.028","volume":"196","author":"JM Bilbao","year":"2009","unstructured":"Bilbao, J.M., Ordo\u00f1ez, M.: Axiomatizations of the Shapley value for games on augmenting systems. Eur. J. Oper. Res. 196, 1008\u20131014 (2009)","journal-title":"Eur. J. Oper. Res."},{"key":"1057_CR26","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1137\/080719170","volume":"24","author":"E Algaba","year":"2010","unstructured":"Algaba, E., Bilbao, J.M., Slikker, M.: A value for games restricted by augmenting systems. SIAM J. Discrete Math. 24, 992\u20131010 (2010)","journal-title":"SIAM J. Discrete Math."},{"key":"1057_CR27","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1006\/jeth.2001.2949","volume":"107","author":"S Ambec","year":"2002","unstructured":"Ambec, S., Sprumont, Y.: Sharing a river. J. Econ. Theory 107, 453\u2013462 (2002)","journal-title":"J. Econ. Theory"},{"key":"1057_CR28","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s10640-012-9566-2","volume":"53","author":"B Dong","year":"2012","unstructured":"Dong, B., Ni, D., Wang, Y.: Sharing a polluted river network. Environ. Resour. Econ. 53, 367\u2013387 (2012)","journal-title":"Environ. Resour. Econ."},{"key":"1057_CR29","doi-asserted-by":"crossref","first-page":"1772","DOI":"10.1137\/110859269","volume":"72","author":"M Gugat","year":"2012","unstructured":"Gugat, M.: Contamination source determination in water distribution networks. SIAM J. Appl. Math. 72, 1772\u20131791 (2012)","journal-title":"SIAM J. Appl. Math."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-1057-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-016-1057-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-1057-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,25]],"date-time":"2017-06-25T08:39:16Z","timestamp":1498379956000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-016-1057-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,19]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["1057"],"URL":"https:\/\/doi.org\/10.1007\/s10957-016-1057-0","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,19]]}}}