发表机构
LIP6; CNRS; Sorbonne Université（巴黎六大计算机实验室; 法国国家科学研究中心; 索邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对树状层次智能体的多级公平资源分配问题，提出三种基于嫉妒的公平概念适配方式，证明相同偏好下MWRR可保证相关概念，一般偏好下MWRR表现有差异，实验显示其对未正式保证的适配仍有良好性能。
AI 中文摘要
我们研究智能体间具有树状层次关系的多级公平资源分配问题。每一层可局部视为将一个智能体的资源束分配给其子节点，整体分配是该过程迭代至叶节点的结果。假设内部节点的效用为其子节点的功利主义福利，且叶节点对物品具有经典加性效用，我们首先对常见的基于嫉妒的公平概念（如WEF1）提出多级适配方案，共提出三种适配方式并证明其选择并非中性。我们证明，在相同偏好下，三种适配的基于嫉妒的概念完全一致，且加权轮询（Chakraborty等人，2021）的多级扩展（MWRR）可保证这些概念的成立。随后我们证明，在一般偏好下，MWRR可能保证部分概念却无法满足其他概念。最后，通过实验表明，即便对于其未正式保证的适配方式，MWRR仍可能表现良好。
英文摘要
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.
CommentsAccepted at the 9th International conference on Algorithmic Decision Theory
