{"type":"ScholarlyArticle","title":"Fair and Efficient Allocation of Indivisible Chores with Surplus","authors":[{"name":"Hannaneh Akrami","slug":"hannaneh-akrami","given":"Hannaneh","family":"Akrami","affiliation":"Max Planck Institute for Informatics , Germany; Graduiertenschule Informatik , Universität des Saarlandes , Germany"},{"name":"Bhaskar Ray Chaudhury","slug":"bhaskar-ray-chaudhury","given":"Bhaskar Ray","family":"Chaudhury","affiliation":"University of Illinois at Urbana-Champaign , USA"},{"name":"Jugal Garg","slug":"jugal-garg","given":"Jugal","family":"Garg","affiliation":"University of Illinois at Urbana-Champaign , USA"},{"name":"Kurt Mehlhorn","slug":"kurt-mehlhorn","given":"Kurt","family":"Mehlhorn","affiliation":"Max Planck Institute for Informatics , Germany"},{"name":"Ruta Mehta","slug":"ruta-mehta","given":"Ruta","family":"Mehta","affiliation":"University of Illinois at Urbana-Champaign , USA"}],"abstract":"We study fair division of indivisible chores among n agents with additive disutility functions. Two well-studied fairness notions for indivisible items are envy-freeness up to one/any item (EF1/EFX) and the standard notion of economic efficiency is Pareto optimality (PO). There is a noticeable gap between the results known for both EF1 and EFX in the goods and chores settings. The case of chores turns out to be much more challenging. We reduce this gap by providing slightly relaxed versions of the known results on goods for the chores setting. Interestingly, our algorithms run in polynomial time, unlike their analogous versions in the goods setting.  \r\n\r\nWe introduce the concept of k surplus in the chores setting which means that up to k more chores are allocated to the agents and each of them is a copy of an original chore. We present a polynomial-time algorithm which gives EF1 and PO allocations with n-1 surplus. \r\n    \r\nWe relax the notion of EFX slightly and define tEFX which requires that the envy from agent i to agent j is removed upon the transfer of any chore from the i's bundle to j's bundle. We give a polynomial-time algorithm that in the chores case for 3 agents returns an allocation which is either proportional or tEFX. Note that proportionality is a very strong criterion in the case of indivisible items, and hence both notions we guarantee are desirable.","doi":"10.24963/ijcai.2023/277","url":"https://ijcai.org/proceedings/2023/277","pdf":"https://ijcai.org/proceedings/2023/0277.pdf","markdown":"https://ijcai.org/proceedings/2023/277.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/277","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":277,"pages":{"first":2494,"last":2502},"keywords":["Game Theory and Economic Paradigms: GTEP: Fair division","Agent-based and Multi-agent Systems: MAS: Resource allocation"],"videos":[],"references":[{"position":1,"raw":"[Akrami et al., 2022a] Hannaneh Akrami, Bhaskar Ray Chaudhury, Jugal Garg, Kurt Mehlhorn, and Ruta Mehta. 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