Breaking the Envy Cycle: Best-of-Both-Worlds Guarantees for Subadditive Valuations

04/07/2023

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by   Michal Feldman, et al.

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We study best-of-both-worlds guarantees for the fair division of indivisible items among agents with subadditive valuations. Our main result establishes the existence of a random allocation that is simultaneously ex-ante 1/2-envy-free, ex-post 1/2-EFX and ex-post EF1, for every instance with subadditive valuations. We achieve this result by a novel polynomial-time algorithm that randomizes the well-established envy cycles procedure in a way that provides ex-ante fairness. Notably, this is the first best-of-both-worlds fairness guarantee for subadditive valuations, even when considering only EF1 without EFX.