# Extension of Additive Valuations to General Valuations on the Existence of EFX

arXiv: https://arxiv.org/abs/2107.09901 · HTML: https://mlsanity.com/paper/2107.09901/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2021.

## Built on by (most cited first, 3 of 3)

- [Understanding EFX Allocations: Counting and Variants](https://mlsanity.com/paper/2504.03951/) (2025)
- [On the existence of EFX allocations in multigraphs](https://mlsanity.com/paper/2502.09777/) (2025)
- [The Cost of EFX: Generalized-Mean Welfare and Complexity Dichotomies with Few Surplus Items](https://mlsanity.com/paper/2601.12849/) (2026)

## Abstract (arXiv)

Envy-freeness is one of the most widely studied notions in fair division. Since envy-free allocations do not always exist when items are indivisible, several relaxations have been considered. Among them, possibly the most compelling concept is envy-freeness up to any item (EFX). We study the existence of EFX allocations for general valuations. The existence of EFX allocations is a major open problem. For general valuations, it is known that an EFX allocation always exists (i) when n=2 or (ii) when all agents have identical valuations, where n is the number of agents. it is also known that an EFX allocation always exists when one can leave at most n-1 items unallocated. We develop new techniques and extend some results of additive valuations to general valuations on the existence of EFX allocations. We show that an EFX allocation always exists (i) when all agents have one of two general valuations or (ii) when the number of items is at most n+3. We also show that an EFX allocation always exists when one can leave at most n-2 items unallocated. In addition to the positive results, we construct an instance with n=3 in which an existing approach does not work as it is.