{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T14:23:57Z","timestamp":1772029437453,"version":"3.50.1"},"reference-count":47,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:00:00Z","timestamp":1559260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100011199","name":"European Research Council","doi-asserted-by":"publisher","award":["291528"],"award-info":[{"award-number":["291528"]}],"id":[{"id":"10.13039\/100011199","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100018237","name":"AOARD","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100018237","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000935","name":"Department of Broadband, Communications and the Digital Economy , Australian Government","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000935","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["BR 2312\/7-1"],"award-info":[{"award-number":["BR 2312\/7-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Econ. Comput."],"published-print":{"date-parts":[[2019,5,31]]},"abstract":"<jats:p>\n            The work we present in this article initiated the formal study of\n            <jats:italic>fractional hedonic games<\/jats:italic>\n            (FHGs), coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which players only distinguish between friends and non-friends and desire to be in a coalition in which the fraction of friends is maximal. FHGs thus not only constitute a natural class of succinctly representable coalition formation games but also provide an interesting framework for network clustering. We propose a number of conditions under which the core of FHGs is non-empty and provide algorithms for computing a core stable outcome. By contrast, we show that the core may be empty in other cases, and that it is computationally hard in general to decide non-emptiness of the core.\n          <\/jats:p>","DOI":"10.1145\/3327970","type":"journal-article","created":{"date-parts":[[2019,6,11]],"date-time":"2019-06-11T13:28:16Z","timestamp":1560259696000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":41,"title":["Fractional Hedonic Games"],"prefix":"10.1145","volume":"7","author":[{"given":"Haris","family":"Aziz","sequence":"first","affiliation":[{"name":"UNSW Sydney and Data61 CSIRO, Sydney NSW, Australia"}]},{"given":"Florian","family":"Brandl","sequence":"additional","affiliation":[{"name":"Technical University of Munich, Munich, Germany"}]},{"given":"Felix","family":"Brandt","sequence":"additional","affiliation":[{"name":"Technical University of Munich, Munich, Germany"}]},{"given":"Paul","family":"Harrenstein","sequence":"additional","affiliation":[{"name":"University of Oxford, Oxford, UK"}]},{"given":"Martin","family":"Olsen","sequence":"additional","affiliation":[{"name":"Aarhus University, Herning, Denmark"}]},{"given":"Dominik","family":"Peters","sequence":"additional","affiliation":[{"name":"University of Oxford, Oxford, UK"}]}],"member":"320","published-online":{"date-parts":[[2019,6,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmateco.2003.12.001"},{"key":"e_1_2_1_2_1","unstructured":"G. Arrhenius J. Ryberg and T. T\u00e4nnsj\u00f6. 2017. The repugnant conclusion. In The Stanford Encyclopedia of Philosophy (Spring 2017 ed.) E. N. Zalta (Ed.). Metaphysics Research Lab Stanford University. https:\/\/plato.stanford.edu\/cgi-bin\/encyclopedia\/archinfo.cgi?entry&equals;repugnant-conclusion.  G. Arrhenius J. Ryberg and T. T\u00e4nnsj\u00f6. 2017. The repugnant conclusion. In The Stanford Encyclopedia of Philosophy (Spring 2017 ed.) E. N. Zalta (Ed.). Metaphysics Research Lab Stanford University. https:\/\/plato.stanford.edu\/cgi-bin\/encyclopedia\/archinfo.cgi?entry&equals;repugnant-conclusion."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2013.08.006"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of the 13th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201914)","author":"Aziz H.","unstructured":"H. Aziz , F. Brandt , and P. Harrenstein . 2014. Fractional hedonic games . In Proceedings of the 13th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201914) . 5--12. H. Aziz, F. Brandt, and P. Harrenstein. 2014. Fractional hedonic games. In Proceedings of the 13th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201914). 5--12."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2012.09.006"},{"key":"e_1_2_1_6_1","volume-title":"Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI\u201915)","author":"Aziz H.","unstructured":"H. Aziz , S. Gaspers , J. Gudmundsson , J. Mestre , and H. T\u00e4ubig . 2015. Welfare maximization in fractional hedonic games . In Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI\u201915) . 461--467. H. Aziz, S. Gaspers, J. Gudmundsson, J. Mestre, and H. T\u00e4ubig. 2015. Welfare maximization in fractional hedonic games. In Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI\u201915). 461--467."},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","unstructured":"H. Aziz and R. Savani. 2016. Hedonic games. In Handbook of Computational Social Choice F. Brandt V. Conitzer U. Endriss J. Lang and A. D. Procaccia (Eds.). Cambridge University Press 356--376.  H. Aziz and R. Savani. 2016. Hedonic games. In Handbook of Computational Social Choice F. Brandt V. Conitzer U. Endriss J. Lang and A. D. Procaccia (Eds.). Cambridge University Press 356--376.","DOI":"10.1017\/CBO9781107446984.016"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917)","author":"Balliu A.","unstructured":"A. Balliu , M. Flammini , G. Melideo , and D. Olivetti . 2017b. Nash stability in social distance games . In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917) . 342--348. A. Balliu, M. Flammini, G. Melideo, and D. Olivetti. 2017b. Nash stability in social distance games. In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917). 342--348."},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917)","author":"Balliu A.","unstructured":"A. Balliu , M. Flammini , and D. Olivetti . 2017a. On Pareto optimality in social distance games . In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917) . 349--355. A. Balliu, M. Flammini, and D. Olivetti. 2017a. On Pareto optimality in social distance games. In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917). 349--355."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s003550000067"},{"key":"e_1_2_1_11_1","volume-title":"Web and Internet Economics. Lecture Notes in Computer Science","volume":"8877","author":"Bil\u00f2 V.","unstructured":"V. Bil\u00f2 , A. Fanelli , M. Flammini , G. Monaco , and L. Moscardelli . 2014. Nash stability in fractional hedonic games . In Web and Internet Economics. Lecture Notes in Computer Science , Vol. 8877 . Springer, 486--491. V. Bil\u00f2, A. Fanelli, M. Flammini, G. Monaco, and L. Moscardelli. 2014. Nash stability in fractional hedonic games. In Web and Internet Economics. Lecture Notes in Computer Science, Vol. 8877. Springer, 486--491."},{"key":"e_1_2_1_12_1","volume-title":"Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201915)","author":"Bil\u00f2 V.","unstructured":"V. Bil\u00f2 , A. Fanelli , M. Flammini , G. Monaco , and L. Moscardelli . 2015. On the price of stability of fractional hedonic games . In Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201915) . 1239--1247. V. Bil\u00f2, A. Fanelli, M. Flammini, G. Monaco, and L. Moscardelli. 2015. On the price of stability of fractional hedonic games. In Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201915). 1239--1247."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1006\/game.2001.0877"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/362686.362694"},{"key":"e_1_2_1_15_1","volume-title":"Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201915)","author":"Brandl F.","unstructured":"F. Brandl , F. Brandt , and M. Strobel . 2015. Fractional hedonic games: Individual and group stability . In Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201915) . 1219--1227. F. Brandl, F. Brandt, and M. Strobel. 2015. Fractional hedonic games: Individual and group stability. In Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201915). 1219--1227."},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI\u201911)","author":"Br\u00e2nzei S.","unstructured":"S. Br\u00e2nzei and K. Larson . 2011. Social distance games . In Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI\u201911) . 273--279. S. Br\u00e2nzei and K. Larson. 2011. Social distance games. In Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI\u201911). 273--279."},{"key":"e_1_2_1_17_1","first-page":"353","article-title":"Computational complexity of stable partitions with B-preferences","volume":"31","author":"Cechl\u00e1rov\u00e1 K.","year":"2002","unstructured":"K. Cechl\u00e1rov\u00e1 and J. Hajdukov\u00e1 . 2002 . Computational complexity of stable partitions with B-preferences . International Journal of Game Theory 31 , 3 (2002), 353 -- 354 . K. Cechl\u00e1rov\u00e1 and J. Hajdukov\u00e1. 2002. Computational complexity of stable partitions with B-preferences. International Journal of Game Theory 31, 3 (2002), 353--354.","journal-title":"International Journal of Game Theory"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s001820000053"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.066111"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1086\/421171"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00355-006-0104-4"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.2307\/1912943"},{"key":"e_1_2_1_23_1","volume-title":"Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI\u201916)","author":"Elkind E.","unstructured":"E. Elkind , A. Fanelli , and M. Flammini . 2016. Price of Pareto optimality in hedonic games . In Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI\u201916) . 475--481. E. Elkind, A. Fanelli, and M. Flammini. 2016. Price of Pareto optimality in hedonic games. In Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI\u201916). 475--481."},{"key":"e_1_2_1_24_1","volume-title":"Proceedings of the 24th ACM Symposium on Parallelism in Algorithms and Architectures. 267--276","author":"Feldman M.","unstructured":"M. Feldman , L. Lewin-Eytan , and J. Naor . 2012. Hedonic clustering games . In Proceedings of the 24th ACM Symposium on Parallelism in Algorithms and Architectures. 267--276 . M. Feldman, L. Lewin-Eytan, and J. Naor. 2012. Hedonic clustering games. In Proceedings of the 24th ACM Symposium on Parallelism in Algorithms and Architectures. 267--276."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2009.11.002"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219198906001144"},{"key":"e_1_2_1_27_1","volume-title":"Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201916)","author":"Igarashi A.","unstructured":"A. Igarashi and E. Elkind . 2016. Hedonic games with graph-restricted communication . In Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201916) . 242--250. A. Igarashi and E. Elkind. 2016. Hedonic games with graph-restricted communication. In Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201916). 242--250."},{"key":"e_1_2_1_28_1","volume-title":"Proceedings of the 9th International Symposium on Algorithmic Game Theory (SAGT\u201916)","volume":"9928","author":"Kaklamanis C.","unstructured":"C. Kaklamanis , P. Kanellopoulos , and K. Papaioannou . 2016. The price of stability of simple symmetric fractional hedonic games . In Proceedings of the 9th International Symposium on Algorithmic Game Theory (SAGT\u201916) , Vol. 9928 . 220--232. C. Kaklamanis, P. Kanellopoulos, and K. Papaioannou. 2016. The price of stability of simple symmetric fractional hedonic games. In Proceedings of the 9th International Symposium on Algorithmic Game Theory (SAGT\u201916), Vol. 9928. 220--232."},{"key":"e_1_2_1_29_1","volume-title":"Minimax and Applications","author":"Ko K.-I.","unstructured":"K.-I. Ko and C.-L. Lin . 1995. On the complexity of min-max optimization problems and their approximation . In Minimax and Applications . Springer , 219--239. K.-I. Ko and C.-L. Lin. 1995. On the complexity of min-max optimization problems and their approximation. In Minimax and Applications. Springer, 219--239."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00355-012-0659-1"},{"key":"e_1_2_1_31_1","volume-title":"Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917)","author":"Liu J.","unstructured":"J. Liu and Z. Wei . 2017. Network, popularity and social cohesion: A game-theoretic approach . In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917) . 600--606. J. Liu and Z. Wei. 2017. Network, popularity and social cohesion: A game-theoretic approach. In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI\u201917). 600--606."},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1006\/game.2001.0878"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2004-00124-y"},{"key":"e_1_2_1_34_1","volume-title":"Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201916)","author":"Nguyen N-T.","unstructured":"N-T. Nguyen , A. Rey , L. Rey , J. Rothe , and L. Schend . 2016. Altruistic hedonic games . In Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201916) . 251--259. N-T. Nguyen, A. Rey, L. Rey, J. Rothe, and L. Schend. 2016. Altruistic hedonic games. In Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS\u201916). 251--259."},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-009-9176-8"},{"key":"e_1_2_1_36_1","volume-title":"Proceedings of the 18th Computing: Australasian Theory Symposium (CATS\u201912)","volume":"128","author":"Olsen M.","year":"2012","unstructured":"M. Olsen . 2012 . On defining and computing communities . In Proceedings of the 18th Computing: Australasian Theory Symposium (CATS\u201912) . Vol. 128 . 97--102. M. Olsen. 2012. On defining and computing communities. In Proceedings of the 18th Computing: Australasian Theory Symposium (CATS\u201912). Vol. 128. 97--102."},{"key":"e_1_2_1_37_1","volume-title":"Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI\u201917)","author":"Ota K.","unstructured":"K. Ota , N. Barrot , A. Ismaili , Y. Sakurai , and M. Yokoo . 2017. Core stability in hedonic games among friends and enemies: Impact of neutrals . In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI\u201917) . 359--365. K. Ota, N. Barrot, A. Ismaili, Y. Sakurai, and M. Yokoo. 2017. Core stability in hedonic games among friends and enemies: Impact of neutrals. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI\u201917). 359--365."},{"key":"e_1_2_1_38_1","unstructured":"D. Parfit. 1984. Reasons and Persons. Oxford University Press.  D. Parfit. 1984. Reasons and Persons. Oxford University Press."},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-67504-6_15"},{"key":"e_1_2_1_40_1","volume-title":"Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI\u201915)","author":"Peters D.","unstructured":"D. Peters and E. Elkind . 2015. Simple causes of complexity in hedonic games . In Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI\u201915) . 617--623. D. Peters and E. Elkind. 2015. Simple causes of complexity in hedonic games. In Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI\u201915). 617--623."},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-015-9461-y"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1080\/0022250X.1971.9989794"},{"key":"e_1_2_1_43_1","unstructured":"T. C. Schelling. 1978. Micromotives and Macrobehavior. W. W. Norton 8 Company.  T. C. Schelling. 1978. Micromotives and Macrobehavior. W. W. Norton 8 Company."},{"key":"e_1_2_1_44_1","volume-title":"Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI\u201917)","author":"Sliwinski J.","unstructured":"J. Sliwinski and Y. Zick . 2017. Learning hedonic games . In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI\u201917) . 2730--2736. J. Sliwinski and Y. Zick. 2017. Learning hedonic games. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI\u201917). 2730--2736."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2009.09.004"},{"key":"e_1_2_1_46_1","unstructured":"E. Weese M. Hayashi and M. Nishikawa. 2017. Inefficiency and self-determination: Simulation-based evidence from Meiji Japan. Working Paper.  E. Weese M. Hayashi and M. Nishikawa. 2017. Inefficiency and self-determination: Simulation-based evidence from Meiji Japan. Working Paper."},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mathsocsci.2012.10.001"}],"container-title":["ACM Transactions on Economics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3327970","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3327970","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:25:33Z","timestamp":1750206333000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3327970"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,31]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,5,31]]}},"alternative-id":["10.1145\/3327970"],"URL":"https:\/\/doi.org\/10.1145\/3327970","relation":{},"ISSN":["2167-8375","2167-8383"],"issn-type":[{"value":"2167-8375","type":"print"},{"value":"2167-8383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,31]]},"assertion":[{"value":"2017-05-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-06-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}