EFX Allocations Exist for Binary Valuations

TL;DR

This paper proves the existence of EFX allocations for binary valuations beyond submodular cases and provides a polynomial-time algorithm for computing such allocations, advancing fair division theory.

Contribution

It extends the existence of EFX allocations to all binary valuations and introduces a polynomial-time algorithm for their computation.

Findings

EFX allocations exist for all binary valuations.

A polynomial-time algorithm for computing EFX allocations is presented.

The result generalizes previous work limited to submodular valuations.

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.