{"type":"ScholarlyArticle","title":"On the Pursuit of EFX for Chores: Non-existence and Approximations","authors":[{"name":"Vasilis Christoforidis","slug":"vasilis-christoforidis","given":"Vasilis","family":"Christoforidis","affiliation":"Archimedes / Athena RC; Aristotle University of Thessaloniki"},{"name":"Christodoulos Santorinaios","slug":"christodoulos-santorinaios","given":"Christodoulos","family":"Santorinaios","affiliation":"Archimedes / Athena RC; Athens University of Economics and Business"}],"abstract":"We study the problem of fairly allocating a set of chores to a group of agents. The existence of envy-free up to any item (EFX) allocations is a long-standing open question for both goods and chores. We resolve this question by providing a negative answer for the latter, presenting a simple construction that admits no EFX solutions for allocating six items to three agents equipped with superadditive cost functions, thus proving a separation result between goods and bads. In fact, we uncover a deeper insight, showing that the instance has unbounded approximation ratio. Moreover, we show that deciding whether an EFX allocation exists is NP-complete. On the positive side, we establish the existence of EFX allocations under general monotone cost functions when the number of items is at most n + 2.  We then shift our attention to additive cost functions. We employ a general framework in order to improve the approximation guarantees in the well-studied case of three additive agents, and provide several conditional approximation bounds that leverage ordinal information.","doi":"10.24963/ijcai.2024/300","url":"https://ijcai.org/proceedings/2024/300","pdf":"https://ijcai.org/proceedings/2024/0300.pdf","markdown":"https://ijcai.org/proceedings/2024/300.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/300","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":300,"pages":{"first":2713,"last":2721},"keywords":["Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Akrami et al., 2023] Hannaneh Akrami, Noga Alon, Bhaskar Ray Chaudhury, Jugal Garg, Kurt Mehlhorn, and Ruta Mehta. 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