# The Frontier of Intractability for EFX with Two Agents

arXiv: https://arxiv.org/abs/2301.10354 · HTML: https://mlsanity.com/paper/2301.10354/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [On the existence of EFX allocations in multigraphs](https://mlsanity.com/paper/2502.09777/) (2025)

## Abstract (arXiv)

We consider the problem of sharing a set of indivisible goods among agents in a fair manner, namely such that the allocation is envy-free up to any good (EFX). We focus on the problem of computing an EFX allocation in the two-agent case and characterize the computational complexity of the problem for most well-known valuation classes. We present a simple greedy algorithm that solves the problem when the agent valuations are weakly well-layered, a class which contains gross substitutes and budget-additive valuations. For the next largest valuation class we prove a negative result: the problem is PLS-complete for submodular valuations. All of our results also hold for the setting where there are many agents with identical valuations.