Two Algorithms for Additive and Fair Division of Mixed Manna

Martin Aleksandrov; Toby Walsh

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arXiv · 2007.04129

Two Algorithms for Additive and Fair Division of Mixed Manna

Martin Aleksandrov·Toby Walsh

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Abstract

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX$_0$, EFX$^3$ and EF1$^3$ - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1$^3$ allocation. With $-\alpha/0/\alpha$ utilities, this algorithm returns an EFX$^3$ and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With $-\alpha/0/\beta$ utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.

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Martin Aleksandrov, Toby Walsh. 2020-07-08. Two Algorithms for Additive and Fair Division of Mixed Manna. https://arxiv.org/abs/2007.04129

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