Unified Fair Allocation of Goods and Chores via Copies
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| Title: | Unified Fair Allocation of Goods and Chores via Copies |
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| Authors: | Yotam Gafni, Xin Huang, Ron Lavi, Inbal Talgam-Cohen |
| Source: | Gafni, Y, Huang, X, Lavi, R & Talgam-Cohen, I 2023, 'Unified Fair Allocation of Goods and Chores via Copies', ACM Transactions on Economics and Computation, vol. 11, no. 3-4, 10. https://doi.org/10.1145/3618116 ACM Transactions on Economics and Computation |
| Publication Status: | Preprint |
| Publisher Information: | Association for Computing Machinery (ACM), 2023. |
| Publication Year: | 2023 |
| Subject Terms: | FOS: Computer and information sciences, name=Marketing, 05 social sciences, resource allocation, 02 engineering and technology, 0102 computer and information sciences, name=Computational Mathematics, 01 natural sciences, Fair division, Computer Science - Computer Science and Game Theory, 0502 economics and business, 0202 electrical engineering, electronic engineering, information engineering, approximate envy-freeness, name=Computer Science (miscellaneous), name=Economics and Econometrics, name=Statistics and Probability, Computer Science and Game Theory (cs.GT) |
| Description: | We consider fair allocation of indivisible items in a model with goods, chores, and copies, as a unified framework for studying: (1) the existence of EFX and other solution concepts for goods with copies; (2) the existence of EFX and other solution concepts for chores. We establish a tight relation between these issues via two conceptual contributions: First, a refinement of envy-based fairness notions that we term envy without commons (denoted EFX WC when applied to EFX). Second, a formal duality theorem relating the existence of a host of (refined) fair allocation concepts for copies to their existence for chores. We demonstrate the usefulness of our duality result by using it to characterize the existence of EFX for chores through the dual environment, as well as to prove EFX existence in the special case of leveled preferences over the chores. We further study the hierarchy among envy-freeness notions without commons and their α-MMS guarantees, showing, for example, that any EFX WC allocation guarantees at least \(\frac{4}{11}\) -MMS for goods with copies. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 2167-8383 2167-8375 |
| DOI: | 10.1145/3618116 |
| DOI: | 10.48550/arxiv.2109.08671 |
| Access URL: | http://arxiv.org/abs/2109.08671 https://purehost.bath.ac.uk/ws/files/303539554/Goods_with_Copies_for_TEAC_R_R_v2_August_Deadline_-2.pdf |
| Rights: | CC BY URL: https://www.acm.org/publications/policies/copyright_policy#Background |
| Accession Number: | edsair.doi.dedup.....19dab35eaffc06e4b0f62e91c1135c2d |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | We consider fair allocation of indivisible items in a model with goods, chores, and copies, as a unified framework for studying: (1) the existence of EFX and other solution concepts for goods with copies; (2) the existence of EFX and other solution concepts for chores. We establish a tight relation between these issues via two conceptual contributions: First, a refinement of envy-based fairness notions that we term envy without commons (denoted EFX WC when applied to EFX). Second, a formal duality theorem relating the existence of a host of (refined) fair allocation concepts for copies to their existence for chores. We demonstrate the usefulness of our duality result by using it to characterize the existence of EFX for chores through the dual environment, as well as to prove EFX existence in the special case of leveled preferences over the chores. We further study the hierarchy among envy-freeness notions without commons and their α-MMS guarantees, showing, for example, that any EFX WC allocation guarantees at least \(\frac{4}{11}\) -MMS for goods with copies. |
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| ISSN: | 21678383 21678375 |
| DOI: | 10.1145/3618116 |