具有元类型的显性资源公平性
Dominant Resource Fairness with Meta-Types
摘要：
受最近COVID-19疫情的启发，我们研究了具有异质需求和Leontief效用的多资源分配问题的推广。与现有设置不同，我们允许每个代理指定要求，仅接受每个资源总供应的子集的分配。这些要求可以以位置限制的形式出现（例如，由于通勤限制，医院只能接受住在附近的志愿者）。这也可以模拟一种类型的替代效应，其中一些代理需要1个单位的资源A \emph{or} B，两者都属于相同的元类型。但是有些代理人特别想要A，而另一些代理人特别想要B。我们提出了一个新的机制，称为主导资源公平性与Meta类型，它决定了分配通过解决少量的线性规划。所提出的方法满足帕累托最优性、无嫉妒性、防策略性以及我们设置的共享激励概念。据我们所知，我们是第一个研究这个问题的制定，提高了现有的工作，捕捉更多的限制，经常出现在现实生活中的情况。最后，我们数值表明，我们的方法比其他方法更好地扩展到大型问题。
英文摘要：
Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities. Unlike existing settings, we allow each agent to specify requirements to only accept allocations from a subset of the total supply for each resource. These requirements can take form in location constraints (e.g. A hospital can only accept volunteers who live nearby due to commute limitations). This can also model a type of substitution effect where some agents need 1 unit of resource A \emph{or} B, both belonging to the same meta-type. But some agents specifically want A, and others specifically want B. We propose a new mechanism called Dominant Resource Fairness with Meta Types which determines the allocations by solving a small number of linear programs. The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and a notion of sharing incentive for our setting. To the best of our knowledge, we are the first to study this problem formulation, which improved upon existing work by capturing more constraints that often arise in real life situations. Finally, we show numerically that our method scales better to large problems than alternative approaches.
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