Weighted envy-freeness for submodular valuations
研究了在代理人具有不同权重（权利）时，如何公平分配不可分割物品。针对次模估值，提出了两类基于无嫉妒的公平概念，并证明可通过推广挑选序列和最大加权纳什福利等规则实现，同时引入基于调和数的福利度量以提供更强的公平保障。
Abstract We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envy-based notions cannot be extended to the case where agents have matroid-rank (i.e., binary submodular) valuations. We propose two families of envy-based notions for matroid-rank and general submodular valuations, one based on the idea of transferability and the other on marginal values. We show that our notions can be satisfied via generalizations of rules such as picking sequences and maximum weighted Nash welfare. In addition, we introduce welfare measures based on harmonic numbers, and show that variants of maximum weighted harmonic welfare offer stronger fairness guarantees than maximum weighted Nash welfare under matroid-rank valuations.