It is often beneficial for agents to pool their resources in order to better accommodate fluctuations in individual demand. Many multi-round resource allocation mechanisms operate in an online manner: in each round, the agents specify their demands for that round, and the mechanism determines a corresponding allocation. In this paper, we focus instead on the offline setting in which the agents specify their demand for each round at the outset. We formulate a specific resource allocation problem in this setting, and design and analyze an associated mechanism based on the solution concept of lexicographic maximin fairness. We present an efficient implementation of our mechanism, and prove that it is Pareto-efficient, envy-free, non-wasteful, resource monotonic, population monotonic, and group strategyproof. We also prove that our mechanism guarantees each agent at least half of the utility that they can obtain by not sharing their resources. We complement these positive results by proving that no maximin fair mechanism can improve on the aforementioned factor of one-half.

中文翻译：

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多轮平等资源共享

代理商将资源集中起来以更好地适应个人需求的波动通常是有益的。许多多轮资源分配机制以在线方式运行：在每一轮中，代理指定他们对该轮的需求，该机制确定相应的分配。在本文中，我们专注于离线设置，其中代理在一开始就指定他们对每一轮的需求。我们在此设置下制定了一个特定的资源分配问题，并基于词典最大化公平的解决方案设计并分析了相关机制。我们提出了我们机制的有效实现，并证明它是帕累托高效、无嫉妒、无浪费、资源单调、人口单调和群体策略证明。我们还证明了我们的机制保证每个代理至少可以通过不共享他们的资源获得一半的效用。我们通过证明没有 maximin fair 机制可以改进上述二分之一的因素来补充这些积极的结果。