Fractional Assignment with $\ell_1$ Preferences

2026-09-16

AI Summary

研究了通过水填充和二次规划两种方法解决n个对象分配给n个代理的问题，以最小化理想分布与实际分布之间的l1距离，同时保证机制的多种优良性质。

Abstract

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.

Problem

• fractional assignment
• ell_1 preferences
• ideal distribution
• unit capacity

Innovation

• fractional assignment
• l_1 distance
• water filling (WF)
• quadratic programming (QP)
• group-strategyproofness