具有 $\ell_1$ 偏好的分数分配
Fractional Assignment with $\ell_1$ Preferences
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中文总结 AI 辅助
本文研究分数分配问题，提出基于注水和二次规划的两种机制，均实现功利最优、无嫉妒和策略证明，且分别具备群体策略证明性和福利鲁棒性优势。
中文摘要 AI 辅助
我们研究了一个分数分配设置，其中 $n$ 个对象被分配给具有单位容量的 $n$ 个智能体，每个智能体指定一个关于对象的理想分布。与经典随机分配不同，这些理想分布不一定是退化的，因为智能体可能偏好对象的混合而非任何单个对象。我们假设智能体寻求最小化其理想分布与所获分布之间的 $\ell_1$ 距离，这等价于最大化两个分布之间的重叠。我们提出了两种机制，一种基于注水（WF），另一种基于二次规划（QP），并证明这两种机制都是功利最优的（因此是帕累托有效的）、无嫉妒的、策略证明的，并满足平等对待平等者。此外，我们强调了每种机制的独特优势：WF机制满足更强的群体策略证明性，而QP机制在平等主义重叠福利方面更具鲁棒性。
英文摘要
We study a fractional assignment setting where $n$ objects are to be assigned to $n$ agents with unit capacity, and each agent specifies an ideal distribution over the objects. Unlike in classic random assignment, these ideal distributions are not necessarily degenerate, as agents may prefer a mixture of objects rather than any single object. We assume that agents seek to minimize the $\ell_1$ distance between their ideal distribution and the distribution they receive, which is equivalent to maximizing the overlap between the two distributions. We propose two mechanisms, one based on water filling (WF) and the other on quadratic programming (QP), and show that both mechanisms are utilitarian-optimal (and hence Pareto efficient), envy-free, strategyproof, and satisfy equal treatment of equals. Moreover, we highlight a distinct advantage of each mechanism: while the WF mechanism satisfies the stronger property of group-strategyproofness, the QP mechanism is more robust in terms of egalitarian overlap welfare.
发表机构
- Chuo University（中央大学）
- National University of Singapore（新加坡国立大学）
- Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。
