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arXiv · 2608.15822

Exact MMS Allocations under Personalized Bivalued Valuations: Goods and Chores

Yuhao Zhang
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Abstract

The maximin share (MMS) is a central fairness benchmark for allocating indivisible goods and chores. We study additive valuations in the personalized bivalued setting, where each agent assigns one of two agent-specific values to every item. Whether exact MMS allocations always exist in this setting has remained a major open question, as highlighted by Ebadian, Peters, and Shah and by Garg, Huang, and Segal-Halevi. We answer this question affirmatively: we prove that exact MMS allocations always exist for both goods and chores and can be computed in polynomial time. Our proof combines a quota-based reformulation with an envelope relaxation, a sparse extreme-point construction, and flow-based rounding that controls the total rounding loss.

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Yuhao Zhang. 2026-08-16. Exact MMS Allocations under Personalized Bivalued Valuations: Goods and Chores. https://arxiv.org/abs/2608.15822

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