The Frontier of Intractability for EFX with Two Agents
Computer Science and Game Theory
2023-07-18 v2 Computational Complexity
Abstract
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.
Keywords
Cite
@article{arxiv.2301.10354,
title = {The Frontier of Intractability for EFX with Two Agents},
author = {Paul W. Goldberg and Kasper Høgh and Alexandros Hollender},
journal= {arXiv preprint arXiv:2301.10354},
year = {2023}
}