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arXiv · 2410.12966

EF1 for Mixed Manna with Unequal Entitlements

Jugal Garg·Eklavya Sharma
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Abstract

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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Jugal Garg, Eklavya Sharma. 2024-10-16. EF1 for Mixed Manna with Unequal Entitlements. https://arxiv.org/abs/2410.12966

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