{"type":"ScholarlyArticle","title":"Optimal Partitions in Additively Separable Hedonic Games","authors":[{"name":"Haris Aziz","slug":"haris-aziz","given":"Haris","family":"Aziz","affiliation":""},{"name":"Felix Brandt","slug":"felix-brandt","given":"Felix","family":"Brandt","affiliation":""},{"name":"Hans Georg Seedig","slug":"hans-georg-seedig","given":"Hans Georg","family":"Seedig","affiliation":""}],"abstract":"We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given partition is Pareto optimal is coNP-complete, even when preferences are symmetric and strict. Moreover, computing a partition with maximum egalitarian or utilitarian social welfare or one which is both Pareto optimal and individually rational is NP-hard. We also prove that checking whether there exists a partition which is both Pareto optimal and envy-free is Σ2p-complete. Even though an envy-free partition and a Nash stable partition are both guaranteed to exist for symmetric preferences, checking whether there exists a partition which is both envy-free and Nash stable is NP-complete.","doi":"10.5591/978-1-57735-516-8/IJCAI11-019","url":"https://ijcai.org/proceedings/2011/19","pdf":"https://ijcai.org/proceedings/2011/0019.pdf","markdown":"https://ijcai.org/proceedings/2011/19.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/19","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":19,"pages":{"first":43,"last":47},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}