带权益的可加混合神物的几乎无妒忌性：确定性与随机保证
Almost Envy-Freeness for Additive Mixed Manna with Entitlements: Deterministic and Randomized Guarantees
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中文总结 AI 辅助
该研究针对带不对称权益的混合神物不可分割物品分配，证明WEF1分配存在且可多项式计算，WEF1T与fPO兼容，通过有限抽签实现期望WEF且分配满足WEF1T，补充了紧刻画。
中文摘要 AI 辅助
我们研究混合神物场景中带不对称权益的智能体间不可分割物品的公平分配问题，其中物品包含 goods（好品）和 chores（劳役）。对于可加估值，我们证明加权无妒忌至多一件物品（WEF1）分配始终存在且可在多项式时间内计算。我们还研究公平且高效的分配，证明对每个混合神物实例，加权无妒忌至多一次转移（WEF1T）与分数帕累托最优（fPO）兼容。我们的不可能性结果表明，从WEF1到WEF1T的放宽是紧的。我们进一步通过有限抽签证明两全其美的结果，保证期望下的加权无妒忌（WEF），且每个实现的分配满足WEF1T，并与现有不可能性结果形成紧的刻画补充。
英文摘要
We investigate the fair allocation of indivisible items among agents with asymmetric entitlements in mixed manna settings, where the items consist of both goods and chores. For additive valuations, we establish that weighted envy-free up to one item (WEF1) allocations always exist and can be computed in polynomial time. We also study fair and efficient allocation and show that weighted envy-freeness up to one transfer (WEF1T) is compatible with fractional Pareto optimality (fPO) for every mixed-manna instance. This relaxation from WEF1 to WEF1T is tight, as demonstrated by our impossibility result. We further show a best-of-both-worlds result via a finite lottery that guarantees weighted envy-freeness (WEF) in expectation, with every realized allocation satisfying WEF1T and achieving the tight characterization complemented by the existing impossibility result.
发表机构
- University of Macau（澳门大学）
- Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））
- Shanghai Jiao Tong University（上海交通大学）
- Nanyang Technological University（南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。
