EFX Allocations Exist for Binary Valuations

• URL: http://arxiv.org/abs/2308.05503v1
• Date: Thu, 10 Aug 2023 11:28:31 GMT
• Title: EFX Allocations Exist for Binary Valuations
• Authors: Xiaolin Bu, Jiaxin Song and Ziqi Yu
• Abstract summary: We study the fair division problem and the existence of allocations satisfying the fairness criterion envy-freeness up to any item (EFX) By using completely different techniques, we extend this existence to general binary valuations that are not necessarily submodular. We present a time algorithm for computing an EFX allocation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the fair division problem and the existence of allocations satisfying the fairness criterion envy-freeness up to any item (EFX). The existence of EFX allocations is a major open problem in the fair division literature. We consider binary valuations where the marginal gain of the value by receiving an extra item is either $0$ or $1$. Babaioff et al. [2021] proved that EFX allocations always exist for binary and submodular valuations. In this paper, by using completely different techniques, we extend this existence result to general binary valuations that are not necessarily submodular, and we present a polynomial time algorithm for computing an EFX allocation.

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