{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,7]],"date-time":"2025-06-07T19:40:02Z","timestamp":1749325202031,"version":"3.41.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T00:00:00Z","timestamp":1720137600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T00:00:00Z","timestamp":1720137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PID2022-138956NB-I00"],"award-info":[{"award-number":["PID2022-138956NB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009042","name":"Universidad de Sevilla","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100009042","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["OR Spectrum"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Cooperative games model situations in which a group of players work together to make a profit. Frequently, in cooperative situations there are dependency or hierarchical relationships between the players, which must be taken into account when allocating the common profit obtained by the grand coalition. Multiple structures have been used in the literature to model those relationships, and several values have been proposed, but there is something in common in all of them: if a player can veto the participation of another in any coalition, then both players will receive the same share of the profit derived from the active cooperation of the vetoed player. In other words, actively cooperating and giving permission to cooperate are equally valued. In many situations this is neither fair nor realistic. In this paper we introduce a family of allocation rules for cooperative games with authorization structure, which reward positional power less than active cooperation.<\/jats:p>","DOI":"10.1007\/s00291-024-00779-7","type":"journal-article","created":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T14:44:46Z","timestamp":1720190686000},"page":"643-666","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Weighing hierarchical power and active contribution in cooperative games with authorization structure"],"prefix":"10.1007","volume":"47","author":[{"given":"Antonio C.","family":"Alarc\u00f3n","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5349-2235","authenticated-orcid":false,"given":"Jos\u00e9 M.","family":"Gallardo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7571-1240","authenticated-orcid":false,"given":"Andr\u00e9s","family":"Jim\u00e9nez-Losada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,5]]},"reference":[{"key":"779_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.disc.2003.10.019","volume":"282","author":"E Algaba","year":"2004","unstructured":"Algaba E, Bilbao JM, van den Brink R, Jim\u00e9nez-Losada A (2004) Cooperative games on antimatroids. Discret Math 282:1\u201315","journal-title":"Discret Math"},{"issue":"4","key":"779_CR2","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/S0893-9659(99)00216-5","volume":"13","author":"DA Ayoshin","year":"2000","unstructured":"Ayoshin DA, Tanaka T (2000) The Shapley value in totally convex multichoice games. Appl Math Lett 13(4):95\u201398","journal-title":"Appl Math Lett"},{"key":"779_CR3","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1057\/s41599-023-01714-x","volume":"10","author":"D Bessey","year":"2023","unstructured":"Bessey D (2023) Hierarchies and decision-making groups: experimental evidence. Humanit Soc Sci 10:198. https:\/\/doi.org\/10.1057\/s41599-023-01714-x","journal-title":"Humanit Soc Sci"},{"key":"779_CR4","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s001860100111","volume":"53","author":"JM Bilbao","year":"2001","unstructured":"Bilbao JM, Driessen THM, Jim\u00e9nez-Losada A, Lebr\u00f3n EA (2001) The Shapley value for games on matroids: the static model. Math Methods Oper Res 53:333\u2013348","journal-title":"Math Methods Oper Res"},{"key":"779_CR5","doi-asserted-by":"publisher","first-page":"1008","DOI":"10.1016\/j.ejor.2008.04.028","volume":"196","author":"JM Bilbao","year":"2009","unstructured":"Bilbao JM, Ord\u00f3\u00f1ez M (2009) Axiomatizations of the Shapley value for games on augmenting systems. Eur J Oper Res 196:1008\u20131014","journal-title":"Eur J Oper Res"},{"key":"779_CR8","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/BF01240150","volume":"21","author":"J Derks","year":"1993","unstructured":"Derks J, Peters H (1993) A Shapley value for games with restricted coalitions. Internat J Game Theory 21:351\u2013366","journal-title":"Internat J Game Theory"},{"key":"779_CR9","volume-title":"Game Theory in Management Accounting","author":"JM Gallardo","year":"2018","unstructured":"Gallardo JM, Jim\u00e9nez N, Jim\u00e9nez-Losada A (2018) A Shapley value for games with authorization structure. In: Mueller D, Trost R (eds) Game Theory in Management Accounting. Contributions to Management Science, Springer, Cham"},{"key":"779_CR10","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/BF01253782","volume":"20","author":"RP Gilles","year":"1992","unstructured":"Gilles RP, Owen G, van den Brink R (1992) Games with permission structures: the conjunctive approach. Internat J Game Theory 20:277\u2013293","journal-title":"Internat J Game Theory"},{"key":"779_CR11","doi-asserted-by":"crossref","unstructured":"Goldscheider R, Jarosz J, Mulhern C (2018) Use of the 25% rule in valuing intellectual property, In: Intellectual property: valuation, exploitation, and infringement damages, John Wiley & Sons 272\u2013290","DOI":"10.1002\/9781119419235.ch17"},{"key":"779_CR12","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1006\/game.1993.1014","volume":"5","author":"C-R Hsiao","year":"1993","unstructured":"Hsiao C-R, Raghavan TES (1993) Shapley value for multichoice cooperative games. Games Econom Behav 5:240\u2013256","journal-title":"Games Econom Behav"},{"issue":"3","key":"779_CR13","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/BF01756292","volume":"16","author":"E Kalai","year":"1987","unstructured":"Kalai E, Samet D (1987) On weighted Shapley values. Internat J Game Theory 16(3):205\u2013222","journal-title":"Internat J Game Theory"},{"key":"779_CR14","first-page":"307","volume":"28","author":"LS Shapley","year":"1953","unstructured":"Shapley LS (1953) A value for n-person games. Ann Math Stud 28:307\u2013317","journal-title":"Ann Math Stud"},{"key":"779_CR15","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/BF01268161","volume":"18","author":"E Winter","year":"1989","unstructured":"Winter E (1989) A value for cooperative games with levels structure of cooperation. Internat J Game Theory 18:227\u2013240","journal-title":"Internat J Game Theory"},{"key":"779_CR16","unstructured":"van den Brink R (1994) Relational power in hierarchical organizations. Ph. D. Thesis"},{"issue":"1","key":"779_CR6","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF01262510","volume":"26","author":"R van den Brink","year":"1997","unstructured":"van den Brink R (1997) An axiomatization of the disjunctive permission value for games with a permission structure. Internat J Game Theory 26(1):27\u201343","journal-title":"Internat J Game Theory"},{"key":"779_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11750-017-0440-9","volume":"25","author":"R van den Brink","year":"2017","unstructured":"van den Brink R (2017) Games with a permission structure- a survey on generalizations and applications. TOP 25:1\u201333","journal-title":"TOP"}],"container-title":["OR Spectrum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-024-00779-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00291-024-00779-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-024-00779-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,7]],"date-time":"2025-06-07T19:18:17Z","timestamp":1749323897000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00291-024-00779-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,5]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["779"],"URL":"https:\/\/doi.org\/10.1007\/s00291-024-00779-7","relation":{},"ISSN":["0171-6468","1436-6304"],"issn-type":[{"type":"print","value":"0171-6468"},{"type":"electronic","value":"1436-6304"}],"subject":[],"published":{"date-parts":[[2024,7,5]]},"assertion":[{"value":"16 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}