EFX Allocations Exist for Binary Valuations
This resolves a major theoretical question in fair division for binary valuations, with practical implications for resource allocation in domains like computing and economics.
The paper tackles the open problem of whether envy-freeness up to any item (EFX) allocations always exist in fair division, proving that they do for general binary valuations and providing a polynomial-time algorithm to compute them.
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.