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EF1 for Mixed Manna with Unequal Entitlements

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arxiv 2410.12966 v1 pith:IJHT5WF4 submitted 2024-10-16 cs.GT

Jugal Garg , Eklavya Sharma This is my paper · ORCID
classification cs.GT
keywords wef1mannamixedagentsalgorithmentitlementsenvy-freenesspolynomial-time
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We study fair division of indivisible mixed manna when agents have unequal entitlements, with weighted envy-freeness up to one item (WEF1) as our primary notion of fairness. We identify several shortcomings of existing techniques to achieve WEF1. Hence, we relax WEF1 to weighted envy-freeness up to 1 transfer (WEF1T), and give a polynomial-time algorithm for achieving it. We also generalize Fisher markets to the mixed manna setting, and use them to get a polynomial-time algorithm for two agents that outputs a WEF1 allocation.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. When One Good Is Not Enough: EF1 and Pareto Optimality Are Not Compatible for Submodular Valuations

    cs.GT 2026-07 conditional novelty 8.0 of 10

    For submodular valuations, a two-agent, eight-good instance exists in which every EF1 allocation is Pareto-dominated, so EF1 and Pareto optimality are incompatible.

  2. Exploring Relations among Fairness Notions in Discrete Fair Division

    cs.GT 2025-02 conditional novelty 7.0 of 10

    The paper establishes a near-complete implication hierarchy among 22 fairness notions for additive and non-additive valuations over goods, chores, and mixed manna, with an automated inference engine.

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