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The Fair Division of Hereditary Set Systems

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A. VettaAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 9, Issue 2

Article No.: 12, Pages 1 - 19

https://doi.org/10.1145/3434410

Published: 09 February 2021 Publication History

Abstract

We consider the fair division of indivisible items using the maximin shares measure. Recent work on the topic has focused on extending results beyond the class of additive valuation functions. In this spirit, we study the case where the items form a hereditary set system. We present a simple algorithm that allocates each agent a bundle of items whose value is at least 0.3666 times the maximin share of the agent. This improves upon the current best known guarantee of 0.2 due to Ghodsi et al. The analysis of the algorithm is almost tight; we present an instance where the algorithm provides a guarantee of at most 0.3738. We also show that the algorithm can be implemented in polynomial time given a valuation oracle for each agent.

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Cited By

Kulkarni PKulkarni RMehta RDastani MSichman JAlechina NDignum V(2024)Approximating APS Under Submodular and XOS Valuations with Binary MarginalsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662961(1057-1065)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662961
Hummel HHetland M(2022)Maximin Shares Under Cardinality ConstraintsMulti-Agent Systems10.1007/978-3-031-20614-6_11(188-206)Online publication date: 11-Dec-2022
https://doi.org/10.1007/978-3-031-20614-6_11
Barman SVerma P(2022)Approximating Nash Social Welfare Under Binary XOS and Binary Subadditive ValuationsWeb and Internet Economics10.1007/978-3-030-94676-0_21(373-390)Online publication date: 1-Jan-2022
https://doi.org/10.1007/978-3-030-94676-0_21
Show More Cited By

Index Terms

The Fair Division of Hereditary Set Systems
1. Theory of computation
  1. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 9, Issue 2

Special Issue on WINE'18: Part 2

June 2021

91 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3446676

Editors:
David Pennock
Microsoft, USA
,
Ilya Segal
Stanford University, USA

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Copyright © 2021 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 February 2021

Accepted: 01 September 2020

Revised: 01 April 2019

Received: 01 April 2019

Published in TEAC Volume 9, Issue 2

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Cited By

Kulkarni PKulkarni RMehta RDastani MSichman JAlechina NDignum V(2024)Approximating APS Under Submodular and XOS Valuations with Binary MarginalsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662961(1057-1065)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662961
Hummel HHetland M(2022)Maximin Shares Under Cardinality ConstraintsMulti-Agent Systems10.1007/978-3-031-20614-6_11(188-206)Online publication date: 11-Dec-2022
https://doi.org/10.1007/978-3-031-20614-6_11
Barman SVerma P(2022)Approximating Nash Social Welfare Under Binary XOS and Binary Subadditive ValuationsWeb and Internet Economics10.1007/978-3-030-94676-0_21(373-390)Online publication date: 1-Jan-2022
https://doi.org/10.1007/978-3-030-94676-0_21
Suksompong W(2021)Constraints in fair divisionACM SIGecom Exchanges10.1145/3505156.350516219:2(46-61)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.1145/3505156.3505162

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