{"type":"ScholarlyArticle","title":"Stable and Envy-free Partitions in Hedonic Games","authors":[{"name":"Nathanaël Barrot","slug":"nathanael-barrot","given":"Nathanaël","family":"Barrot","affiliation":"Riken , AIP Center; Kyushu University"},{"name":"Makoto Yokoo","slug":"makoto-yokoo","given":"Makoto","family":"Yokoo","affiliation":"Kyushu University; Riken , AIP Center"}],"abstract":"In this paper, we study coalition formation in hedonic games through the fairness criterion of envy-freeness. \r\nSince the grand coalition is always envy-free, we focus on the conjunction of envy-freeness with stability notions.\r\nWe first show that, in symmetric and additively separable hedonic games, an individually stable and justified envy-free partition may not exist and deciding its existence is NP-complete.\r\nThen, we prove that the top responsiveness property guarantees the existence of a Pareto optimal, individually stable, and envy-free partition, but it is not sufficient for the conjunction of core stability and envy-freeness.\r\nFinally, under bottom responsiveness, we show that deciding the existence of an individually stable and envy-free partition is NP-complete, but a Pareto optimal and justified envy-free partition always exists.","doi":"10.24963/ijcai.2019/10","url":"https://ijcai.org/proceedings/2019/10","pdf":"https://ijcai.org/proceedings/2019/0010.pdf","markdown":"https://ijcai.org/proceedings/2019/10.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/10","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":10,"pages":{"first":67,"last":73},"keywords":["Agent-based and Multi-agent Systems: Cooperative Games","Agent-based and Multi-agent Systems: Algorithmic Game Theory"],"videos":[],"references":[{"position":1,"raw":"[Abdulkadiroglu and Sönmez, 2003] Atila Abdulkadiroglu and Tayfun Sönmez. 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