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首页> 外文期刊>ACM transactions on economics and computation >Finding Fair and Efficient Allocations for Matroid Rank Valuations
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Finding Fair and Efficient Allocations for Matroid Rank Valuations

机译：为拟阵找到公平和有效的分配排名的估值

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摘要

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions. This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envyfreeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfaremaximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.
机译：在本文中,我们目前的新结果公平和有效的分配不可分割偏好对应的货物代理拟阵秩函数。估值类与几个理想的属性(如单调性和submodularity)自然适用于现实世界域。优势;估值拟阵秩函数,一个社会最优(即,功利主义的社会welfare-maximizing)分配实现envyfreeness一项(EF1)存在,计算处理。纳什welfaremaximizing leximin分配两个展览这公平/效率通过展示,他们可以实现结合通过最小化任何对称严格凸功能实用的最优结果。我们所知,这是第一估值函数类不包含添加剂它的估值已经建立一个分配EF1纳什福利最大化。此外,这些估值的一个子类基于最大(无关紧要的)一式两份的功能匹配,我们表明leximin分配在多项式时间内计算。探索可能的扩展的结果除了EF1以及公平标准归纳上述估值类。

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