Weighted Envy-Freeness in Indivisible Item Allocation

Mithun Chakraborty, Ayumi Igarashi, Warut Suksompong and Yair Zick

Papers from arXiv.org

Abstract: We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where envy can be eliminated by removing an item from the envied agent's bundle, and weak, where envy can be eliminated either by removing an item (as in the strong version) or by replicating an item from the envied agent's bundle in the envying agent's bundle. We show that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists and can be computed in pseudo-polynomial time; moreover, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1, but always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work highlights several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart.

Date: 2019-09, Revised 2021-03
New Economics Papers: this item is included in nep-des, nep-gen and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Published in ACM Transactions on Economics and Computation, 9(3):18 (2021)

Downloads: (external link)
http://arxiv.org/pdf/1909.10502 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1909.10502

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().