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Article . 2021
License: CC BY
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Unified Fair Allocation of Goods and Chores via Copies

Authors: Yotam Gafni; Xin Huang; Ron Lavi; Inbal Talgam-Cohen;

Unified Fair Allocation of Goods and Chores via Copies

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.

Keywords

FOS: Computer and information sciences, /dk/atira/pure/subjectarea/asjc/1400/1406; name=Marketing, resource allocation, /dk/atira/pure/subjectarea/asjc/2600/2605; name=Computational Mathematics, Fair division, Computer Science - Computer Science and Game Theory, approximate envy-freeness, /dk/atira/pure/subjectarea/asjc/1700/1701; name=Computer Science (miscellaneous), /dk/atira/pure/subjectarea/asjc/2000/2002; name=Economics and Econometrics, /dk/atira/pure/subjectarea/asjc/2600/2613; name=Statistics and Probability, Computer Science and Game Theory (cs.GT)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green