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We study the fair division problem and the existence of allocationssatisfying the fairness criterion envy-freeness up to any item (EFX). Theexistence of EFX allocations is a major open problem in the fair divisionliterature. We consider binary valuations where the marginal gain of the valueby receiving an extra item is either $0$ or $1$. Babaioff et al. [2021] provedthat EFX allocations always exist for binary and submodular valuations. In thispaper, by using completely different techniques, we extend this existenceresult to general binary valuations that are not necessarily submodular, and wepresent a polynomial time algorithm for computing an EFX allocation.

EFX Allocations Exist for Binary Valuations