{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T10:34:09Z","timestamp":1777286049193,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T00:00:00Z","timestamp":1648166400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T00:00:00Z","timestamp":1648166400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: strong compromise admissibility and compromise stability. These two properties allow for a direct, closed formula for the nucleolus. We characterize the families of graphs for which the graph-restricted games inherit these properties from the underlying games. Moreover, for each of these two properties, we characterize the family of graphs for which the nucleolus is invariant<\/jats:p>","DOI":"10.1007\/s10479-022-04638-y","type":"journal-article","created":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T03:02:30Z","timestamp":1648177350000},"page":"1117-1135","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The nucleolus and inheritance of properties in communication situations"],"prefix":"10.1007","volume":"318","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7446-4591","authenticated-orcid":false,"given":"J.","family":"Schouten","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8023-0273","authenticated-orcid":false,"given":"B.","family":"Dietzenbacher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2710-1827","authenticated-orcid":false,"given":"P.","family":"Borm","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,25]]},"reference":[{"key":"4638_CR1","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s001860100159","volume":"54","author":"E Algaba","year":"2001","unstructured":"Algaba, E., Bilbao, J., Borm, P., & L\u00f3pez, J. (2001). The Myerson value for union stable structures. Mathematical Methods of Operations Research, 54, 359\u2013371.","journal-title":"Mathematical Methods of Operations Research"},{"key":"4638_CR2","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, J., van den Brink, R., & Jim\u00e9nez-Losada, A. (2004). Cooperative games on antimatroids. Discrete Mathematics, 282, 1\u201315.","journal-title":"Discrete Mathematics"},{"key":"4638_CR3","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1023\/A:1010344404281","volume":"50","author":"E Algaba","year":"2001","unstructured":"Algaba, E., Bilbao, J., & L\u00f3pez, J. (2001). A unified approach to restricted games. Theory and Decision, 50, 333\u2013345.","journal-title":"Theory and Decision"},{"key":"4638_CR4","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/0022-0531(85)90102-4","volume":"36","author":"R Aumann","year":"1985","unstructured":"Aumann, R., & Maschler, M. (1985). Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory, 36, 195\u2013213.","journal-title":"Journal of Economic Theory"},{"key":"4638_CR5","doi-asserted-by":"crossref","unstructured":"Brink, R. van den, Khmelnitskaya, A., & van der Laan, G. (2016). An Owen-type value for games with two-level communication structure. Annals of operations research, 243, 179\u2013198.","DOI":"10.1007\/s10479-015-1808-6"},{"key":"4638_CR6","doi-asserted-by":"crossref","unstructured":"Brink, R. van den, & Pint\u00e9r, M. (2015). On axiomatizations of the Shapley value for assignment games. Journal of Mathematical Economics, 60, 110\u2013114.","DOI":"10.1016\/j.jmateco.2015.06.016"},{"key":"4638_CR7","first-page":"143","volume":"31","author":"I Curiel","year":"1987","unstructured":"Curiel, I., Maschler, M., & Tijs, S. (1987). Bankruptcy games. Zeitschrift f\u00fcr Operations Research, 31, 143\u2013159.","journal-title":"Zeitschrift f\u00fcr Operations Research"},{"key":"4638_CR8","doi-asserted-by":"crossref","unstructured":"Driessen, T. (1988). Cooperative games, solutions and applications. Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-7787-8"},{"key":"4638_CR9","doi-asserted-by":"crossref","unstructured":"Gillies, D. (1959). Solutions to general non-zero-sum games. In A. Tucker & R. Luce (Eds.), Contributions to the theory of games IV (pp. 47\u201386). Princeton University Press.","DOI":"10.1515\/9781400882168-005"},{"key":"4638_CR10","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.mathsocsci.2012.12.006","volume":"66","author":"I Katsev","year":"2013","unstructured":"Katsev, I., & Yanovskaya, E. (2013). The prenucleolus for games with restricted cooperation. Mathematical Social Sciences, 66, 56\u201365.","journal-title":"Mathematical Social Sciences"},{"key":"4638_CR11","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/s00186-013-0444-7","volume":"78","author":"A Khmelnitskaya","year":"2013","unstructured":"Khmelnitskaya, A., & Sudh\u00f6lter, P. (2013). The prenucleolus and the prekernel for games with communication structures. Mathematical Methods of Operations Research, 78, 285\u2013299.","journal-title":"Mathematical Methods of Operations Research"},{"key":"4638_CR12","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1137\/0120009","volume":"20","author":"E Kohlberg","year":"1971","unstructured":"Kohlberg, E. (1971). On the nucleolus of a characteristic function game. SIAM Journal on Applied Mathematics, 20, 62\u201366.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"4638_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10479-020-03825-z","volume":"301","author":"C Manuel","year":"2021","unstructured":"Manuel, C., & Mart\u00edn, D. (2021). A value for communication situations with players having different bargaining abilities. Annals of Operations Research, 301, 161\u2013182.","journal-title":"Annals of Operations Research"},{"key":"4638_CR14","first-page":"303","volume":"39","author":"S Muto","year":"1988","unstructured":"Muto, S., Nakayama, M., Potters, J., & Tijs, S. (1988). On big boss games. The Economic Studies Quarterly, 39, 303\u2013321.","journal-title":"The Economic Studies Quarterly"},{"key":"4638_CR15","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1287\/moor.2.3.225","volume":"2","author":"R Myerson","year":"1977","unstructured":"Myerson, R. (1977). Graphs and cooperation in games. Mathematics of Operations Research, 2, 225\u2013229.","journal-title":"Mathematics of Operations Research"},{"key":"4638_CR16","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/BF01781371","volume":"9","author":"R Myerson","year":"1980","unstructured":"Myerson, R. (1980). Conference structures and fair allocation rules. International Journal of Game Theory, 9, 169\u2013182.","journal-title":"International Journal of Game Theory"},{"key":"4638_CR17","doi-asserted-by":"crossref","unstructured":"Nouweland, A. van den, & Borm, P. (1991). On the convexity of communication games. International Journal of Game Theory, 19, 421\u2013430.","DOI":"10.1007\/BF01766431"},{"key":"4638_CR18","doi-asserted-by":"crossref","unstructured":"Nouweland, A. van den, Borm, P., & Tijs, S. (1992). Allocation rules for hypergraph communication situations. International Journal of Game Theory, 20, 255\u2013268.","DOI":"10.1007\/BF01253780"},{"key":"4638_CR19","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/0165-4896(82)90029-4","volume":"2","author":"B O\u2019Neill","year":"1982","unstructured":"O\u2019Neill, B. (1982). A problem of rights arbitration from the Talmud. Mathematical Social Sciences, 2, 345\u2013371.","journal-title":"Mathematical Social Sciences"},{"key":"4638_CR20","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1137\/0607025","volume":"7","author":"G Owen","year":"1986","unstructured":"Owen, G. (1986). Values of graph-restricted games. SIAM Journal on Algebraic and Discrete Methods, 7, 210\u2013220.","journal-title":"SIAM Journal on Algebraic and Discrete Methods"},{"key":"4638_CR21","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0899-8256(89)90013-4","volume":"1","author":"J Potters","year":"1989","unstructured":"Potters, J., Poos, R., Tijs, S., & Muto, S. (1989). Clan games. Games and Economic Behavior, 1, 275\u2013293.","journal-title":"Games and Economic Behavior"},{"key":"4638_CR22","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/BF01258203","volume":"24","author":"J Potters","year":"1995","unstructured":"Potters, J., & Reijnierse, H. (1995). $$\\Gamma $$-component additive games. International Journal of Game Theory, 24, 49\u201356.","journal-title":"International Journal of Game Theory"},{"key":"4638_CR23","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/s00182-005-0210-z","volume":"33","author":"M Quant","year":"2005","unstructured":"Quant, M., Borm, P., Reijnierse, H., & van Velzen, B. (2005). The core cover in relation to the nucleolus and the Weber set. International Journal of Game Theory, 33, 491\u2013503.","journal-title":"International Journal of Game Theory"},{"key":"4638_CR24","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1006\/game.1997.0629","volume":"24","author":"H Reijnierse","year":"1998","unstructured":"Reijnierse, H., & Potters, J. (1998). The $${\\cal{B}}$$-nucleolus of TU-games. Games and Economic Behavior, 24, 77\u201396.","journal-title":"Games and Economic Behavior"},{"key":"4638_CR25","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1137\/0117107","volume":"17","author":"D Schmeidler","year":"1969","unstructured":"Schmeidler, D. (1969). The nucleolus of a characteristic function game. SIAM Journal on Applied Mathematics, 17, 1163\u20131170.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"4638_CR26","first-page":"307","volume":"28","author":"L Shapley","year":"1953","unstructured":"Shapley, L. (1953). A value for n-person games. Annals of Mathematics Studies, 28, 307\u2013317.","journal-title":"Annals of Mathematics Studies"},{"key":"4638_CR27","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s001820000039","volume":"29","author":"M Slikker","year":"2000","unstructured":"Slikker, M. (2000). Inheritance of properties in communication situations. International Journal of Game Theory, 29, 241\u2013268.","journal-title":"International Journal of Game Theory"},{"key":"4638_CR28","unstructured":"Tijs, S. (1981). Bounds for the core of a game and the $$\\tau $$-value. In O. Moeschlin & D. Pallaschke (Eds.), Game Theory and Mathematical Economics (pp. 123\u2013132). Amsterdam: North-Holland Publishing Company."},{"key":"4638_CR29","first-page":"27","volume":"24","author":"S Tijs","year":"1982","unstructured":"Tijs, S., & Lipperts, F. (1982). The hypercube and the core cover of N-person cooperative games. Cahiers du Centre d\u2019\u00c9tudes de Recherche Op\u00e9rationnelle, 24, 27\u201337.","journal-title":"Cahiers du Centre d\u2019\u00c9tudes de Recherche Op\u00e9rationnelle"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04638-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-022-04638-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04638-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T22:02:50Z","timestamp":1668031370000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-022-04638-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,25]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["4638"],"URL":"https:\/\/doi.org\/10.1007\/s10479-022-04638-y","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,25]]},"assertion":[{"value":"21 February 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}