{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T18:09:23Z","timestamp":1778263763319,"version":"3.51.4"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T00:00:00Z","timestamp":1754438400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T00:00:00Z","timestamp":1754438400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"JST ERATO","award":["JPMJER2301"],"award-info":[{"award-number":["JPMJER2301"]}]},{"name":"JSPS KAKENHI","award":["JP21H04979"],"award-info":[{"award-number":["JP21H04979"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Game Theory"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s00182-025-00952-4","type":"journal-article","created":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T16:42:16Z","timestamp":1754498536000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sharing values for multi-choice games: an axiomatic approach"],"prefix":"10.1007","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9456-790X","authenticated-orcid":false,"given":"David","family":"Lowing","sequence":"first","affiliation":[]},{"given":"Makoto","family":"Yokoo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,6]]},"reference":[{"key":"952_CR1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10479-012-1150-1","volume":"196","author":"S B\u00e9al","year":"2012","unstructured":"B\u00e9al S, Lardon A, R\u00e9mila E, Solal P (2012) The average tree solution for multi-choice forest games. Ann Oper Res 196:27\u201351","journal-title":"Ann Oper Res"},{"key":"952_CR2","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s00355-019-01229-y","volume":"55","author":"M Besner","year":"2020","unstructured":"Besner M (2020) Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set. Soc Choice Welf 55:193\u2013212","journal-title":"Soc Choice Welf"},{"key":"952_CR3","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1007\/s00182-019-00701-4","volume":"49","author":"M Besner","year":"2020","unstructured":"Besner M (2020) Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution. Int J Game Theory 49:851\u2013873","journal-title":"Int J Game Theory"},{"key":"952_CR4","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s10479-020-03576-x","volume":"301","author":"R Branzei","year":"2021","unstructured":"Branzei R, Guti\u00e9rrez E, Llorca N, S\u00e1nchez-Soriano J (2021) Does it make sense to analyse a two-sided market as a multi-choice game? Ann Oper Res 301:17\u201340","journal-title":"Ann Oper Res"},{"key":"952_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1086\/466560","volume":"3","author":"RH Coase","year":"1960","unstructured":"Coase RH (1960) The problem of social cost. J Law Econ 3:1\u201344","journal-title":"J Law Econ"},{"key":"952_CR6","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/BF01245457","volume":"21","author":"J Derks","year":"1992","unstructured":"Derks J (1992) A short proof of the inclusion of the core in the weber set. Int J Game Theory 21:149\u2013150","journal-title":"Int J Game Theory"},{"key":"952_CR7","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s001820050003","volume":"29","author":"J Derks","year":"2000","unstructured":"Derks J, Haller H, Peters H (2000) The selectope for cooperative games. Int J Game Theory 29:23\u201338","journal-title":"Int J Game Theory"},{"key":"952_CR8","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s00186-006-0063-7","volume":"64","author":"J Derks","year":"2006","unstructured":"Derks J, van der Laan G, Vasil\u2019ev V (2006) Characterizations of the random order values by Harsanyi payoff vectors. Math Methods Oper Res 64:155\u2013163","journal-title":"Math Methods Oper Res"},{"key":"952_CR9","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. Int J Game Theory 21:351\u2013360","journal-title":"Int J Game Theory"},{"key":"952_CR10","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s00186-007-0159-8","volume":"66","author":"M Grabisch","year":"2007","unstructured":"Grabisch M, Xie L (2007) A new approach to the core and weber set of multichoice games. Math Methods Oper Res 66:491\u2013512","journal-title":"Math Methods Oper Res"},{"issue":"1\u20132","key":"952_CR11","first-page":"159","volume":"19","author":"P Hammer","year":"1977","unstructured":"Hammer P, Peled U, Sorensen S (1977) Pseudo-Boolean functions and game theory. Core Elem Shapley Value 19(1\u20132):159\u2013176","journal-title":"Core Elem Shapley Value"},{"key":"952_CR12","first-page":"325","volume-title":"Contributions to the theory of games","author":"J Harsanyi","year":"1959","unstructured":"Harsanyi J (1959) A bargaining model for cooperative n-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games, vol 40. Princeton University Press, Princeton, pp 325\u2013355"},{"key":"952_CR13","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/BF01258281","volume":"21","author":"CR Hsiao","year":"1992","unstructured":"Hsiao CR, Raghavan T (1992) Monotonicity and dummy free property for multi-choice cooperative games. Int J Game Theory 21:301\u2013312","journal-title":"Int J Game Theory"},{"key":"952_CR14","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s10898-008-9392-9","volume":"45","author":"YA Hwang","year":"2009","unstructured":"Hwang YA, Liao YH (2009) Equivalence theorem, consistency and axiomatizations of a multi-choice value. J Global Optim 45:597\u2013613","journal-title":"J Global Optim"},{"key":"952_CR15","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. Int J Game Theory 16:205\u2013222","journal-title":"Int J Game Theory"},{"key":"952_CR16","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/s001820050123","volume":"28","author":"F Klijn","year":"1999","unstructured":"Klijn F, Slikker M, Zarzuelo J (1999) Characterizations of a multi-choice value. Int J Game Theory 28:521\u2013532","journal-title":"Int J Game Theory"},{"key":"952_CR17","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1007\/s00355-022-01412-8","volume":"59","author":"D Lowing","year":"2022","unstructured":"Lowing D, Techer K (2022) Marginalism, egalitarianism and efficiency in multi-choice games. Soc Choice Welf 59:815\u2013861","journal-title":"Soc Choice Welf"},{"key":"952_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmateco.2022.102740","volume":"102","author":"D Lowing","year":"2022","unstructured":"Lowing D, Techer K (2022) Priority relations and cooperation with multiple activity levels. J Math Econ 102:102740","journal-title":"J Math Econ"},{"key":"952_CR19","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF01240250","volume":"21","author":"D Monderer","year":"1992","unstructured":"Monderer D, Samet D, Shapley LS (1992) Weighted values and the core. Int J Game Theory 21:27\u201339","journal-title":"Int J Game Theory"},{"key":"952_CR21","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s10479-005-2270-7","volume":"137","author":"H Peters","year":"2005","unstructured":"Peters H, Zank H (2005) The egalitarian solution for multichoice games. Ann Oper Res 137:399\u2013409","journal-title":"Ann Oper Res"},{"key":"952_CR22","first-page":"307","volume":"2","author":"LS Shapley","year":"1953","unstructured":"Shapley LS (1953) A value for n-person games. Contrib Theory of Games 2:307\u2013317","journal-title":"Contrib Theory of Games"},{"key":"952_CR23","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.mathsocsci.2021.04.003","volume":"111","author":"K Techer","year":"2021","unstructured":"Techer K (2021) Stable agreements through liability rules: a multi-choice game approach to the social cost problem. Math Soc Sci 111:77\u201388","journal-title":"Math Soc Sci"},{"key":"952_CR20","volume-title":"Games and graphs in economic situations","author":"CGA van den Nouweland","year":"1993","unstructured":"van den Nouweland CGA (1993) Games and graphs in economic situations. Tilburg University, Tilburg"},{"key":"952_CR24","unstructured":"Vasil\u2019ev V, van der Laan G (2001) The Harsanyi set for cooperative TU-games. Technical Report, Tinbergen Institute Discussion Paper"},{"key":"952_CR25","unstructured":"Vasil\u2019ev VA (1981) On a class of imputations in cooperative games. In: Doklady Akademii Nauk, Russian Academy of Sciences, pp 265\u2013268"},{"key":"952_CR26","first-page":"30","volume":"21","author":"V Vasil\u2019ev","year":"1978","unstructured":"Vasil\u2019ev V (1978) Support function of the core of a convex game. Optim Vyp 21:30\u201335","journal-title":"Optim Vyp"},{"key":"952_CR27","doi-asserted-by":"crossref","unstructured":"Weber RJ (1988) Probabilistic values for games. The Shapley Value. Essays in Honor of Lloyd S. Shapley, pp 101\u2013119","DOI":"10.1017\/CBO9780511528446.008"}],"container-title":["International Journal of Game Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-025-00952-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00182-025-00952-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-025-00952-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T08:27:50Z","timestamp":1766305670000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00182-025-00952-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,6]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["952"],"URL":"https:\/\/doi.org\/10.1007\/s00182-025-00952-4","relation":{},"ISSN":["0020-7276","1432-1270"],"issn-type":[{"value":"0020-7276","type":"print"},{"value":"1432-1270","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,6]]},"assertion":[{"value":"30 June 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"30"}}