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Title: Fair division of mixed divisible and indivisible goods
Authors: Bei, Xiaohui 
Li, Zhihao
Liu, Jinyan
Liu, Shengxin
Lu, Xinhang
Keywords: Science::Mathematics
Issue Date: 2021
Source: Bei, X., Li, Z., Liu, J., Liu, S. & Lu, X. (2021). Fair division of mixed divisible and indivisible goods. Artificial Intelligence, 293, 103436-.
Project: RG23/20
Journal: Artificial Intelligence
Abstract: We study the problem of fair division when the set of resources contains both divisible and indivisible goods. Classic fairness notions such as envy-freeness (EF) and envy-freeness up to one good (EF1) cannot be directly applied to this mixed goods setting. In this work, we propose a new fairness notion, envy-freeness for mixed goods (EFM), which is a direct generalization of both EF and EF1 to the mixed goods setting. We prove that an EFM allocation always exists for any number of agents with additive valuations. We also propose efficient algorithms to compute an EFM allocation for two agents with general additive valuations and for n agents with piecewise linear valuations over the divisible goods. Finally, we relax the envy-freeness requirement, instead asking for ε-envy-freeness for mixed goods (ε-EFM), and present an efficient algorithm that finds an ε-EFM allocation.
ISSN: 0004-3702
DOI: 10.1016/j.artint.2020.103436
Schools: School of Physical and Mathematical Sciences 
Rights: © 2020 Elsevier B.V. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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