Multilevel Fair Allocation under Additive Preferences

2026-08-25

AI Summary

研究了具有树状层级关系的多级公平资源分配问题，提出并比较了多种适应性嫉妒公平概念，并评估了MWRR算法在不同条件下的表现。

Abstract

We study multilevel fair resource allocation with tree-structured hierarchical relations among agents. At each level, the problem can be viewed locally as allocating an agent's bundle to its children, the overall allocation being a trace of this process iterated down to the leaves. Assuming that internal nodes' utilities are the utilitarian welfare of their children, and the leaves have classical additive utilities over items, we first propose multilevel adaptations of usual envy-based fairness notions (e.g., WEF1). We present three adaptations and show that the choice among them is not neutral. We prove that, under identical preferences, the three adapted envy-based notions coincide, and that the Multilevel extension of Weighted Round Robin (Chakraborty et al., 2021) (MWRR) guarantees them. We then show that under general preferences, MWRR may guarantee some notions while failing others. Finally, through experiments, we show that MWRR may still perform well even for adaptations it does not formally guarantee.

Problem

• Multilevel Fair Allocation
• Tree-structured Hierarchical Relations
• Additive Preferences

Innovation

• Multilevel Fair Allocation
• Tree-structured Hierarchical Relations
• Weighted Round Robin (MWRR)
• Envy-based Fairness Notions