Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Zhang, Yuhao
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7203684159