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.
CITATION STYLE
Goldberg, P. W., Høgh, K., & Hollender, A. (2023). The Frontier of Intractability for EFX with Two Agents. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 14238 LNCS, pp. 290–307). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-43254-5_17
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