Fair-Share Allocations for Agents with Arbitrary Entitlements

• 成果类型: Article
• 署名作者: Babaioff, Moshe; Ezra, Tomer; Feige, Uriel
• 署名单位: Hebrew University of Jerusalem; Sapienza University Rome; Weizmann Institute of Science
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.0199
• 发表日期: 2024
• 页码: 2180-2211
• 关键词: competitive-equilibrium

摘要

We consider the problem of fair allocation of indivisible goods to n agents with no transfers. When agents have equal entitlements, the well-established notion of the maxi min share (MMS) serves as an attractive fairness criterion for which, to qualify as fair, an allocation needs to give every agent at least a substantial fraction of the agent's MMS. In this paper, we consider the case of arbitrary (unequal) entitlements. We explain shortcomings in previous attempts that extend the MMS to unequal entitlements. Our conceptual contribution is the introduction of a new notion of a share, the AnyPrice share (APS), that is appropriate for settings with arbitrary entitlements. Even for the equal entitlements case, this notion is new and satisfies APSPMMS, for which the inequality is sometimes strict. We present two equivalent definitions for the APS (one as a minimization problem, the other as a maximization problem) and provide comparisons between the APS and previous notions of fairness. Our main result concerns additive valuations and arbitrary entitlements, for which we provide a polynomial-time algorithm that gives every agent at least a 3 5 fraction of the