Almost Full EFX Exists for Four Agents

Ben Berger, Avi Cohen, Michal Feldman, Amos Fiat

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The existence of EFX allocations of goods is a major open problem in fair division, even for additive valuations. The current state of the art is that no setting where EFX allocations are impossible is known, and yet, existence results are known only for very restricted settings, such as: (i) agents with identical valuations, (ii) 2 agents, and (iii) 3 agents with additive valuations. It is also known that EFX exists if one can leave n − 1 items unallocated, where n is the number of agents. We develop new techniques that allow us to push the boundaries of the enigmatic EFX problem beyond these known results, and (arguably) to simplify proofs of earlier results. Our main result is that every setting with 4 additive agents admits an EFX allocation that leaves at most a single item unallocated. Beyond our main result, we introduce a new class of valuations, termed nice cancelable, which includes additive, unit-demand, budget-additive and multiplicative valuations, among others. Using our new techniques, we show that both our results and previous results for additive valuations extend to nice cancelable valuations.

Original languageEnglish
Title of host publicationAAAI-22 Technical Tracks 5
PublisherAssociation for the Advancement of Artificial Intelligence
Number of pages8
ISBN (Electronic)1577358767, 9781577358763
StatePublished - 30 Jun 2022
Event36th AAAI Conference on Artificial Intelligence, AAAI 2022 - Virtual, Online
Duration: 22 Feb 20221 Mar 2022

Publication series

NameProceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022


Conference36th AAAI Conference on Artificial Intelligence, AAAI 2022
CityVirtual, Online


FundersFunder number
Horizon 2020 Framework Programme
European Research Council
Israel Science Foundation317/17
Horizon 2020866132

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