{"type":"ScholarlyArticle","title":"Settling the Complexity of Popularity in Additively Separable and Fractional Hedonic Games","authors":[{"name":"Martin Bullinger","slug":"martin-bullinger","given":"Martin","family":"Bullinger","affiliation":""},{"name":"Matan Gilboa","slug":"matan-gilboa","given":"Matan","family":"Gilboa","affiliation":""}],"abstract":"We study coalition formation in the framework of hedonic games. These games model the problem of partitioning a set of agents having a preference order over the coalitions they can be part of. A partition is called popular if it does not lose a majority vote among the agents against any other partition. Unfortunately, hedonic games need not admit popular partitions. We go further and settle the complexity of the existence problem concerning popularity in additively separable and fractional hedonic games by showing that it is Sigma_2^p-complete in both cases. We are thus the first work that proves a completeness result of popularity for the second level of the polynomial hierarchy.","doi":"10.24963/ijcai.2025/419","url":"https://ijcai.org/proceedings/2025/419","pdf":"https://ijcai.org/proceedings/2025/0419.pdf","markdown":"https://ijcai.org/proceedings/2025/419.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/419","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":419,"pages":{"first":3771,"last":3779},"keywords":["Game Theory and Economic Paradigms: GTEP: Cooperative games","Game Theory and Economic Paradigms: GTEP: Computational social choice"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}