We study non-monetary mechanisms for the fair and efficient allocation of reusable public resources, i.e., resources used for varying durations. We consider settings where a limited resource is repeatedly shared among a set of agents, each of whom may request to use the resource over multiple consecutive rounds, receiving utility only if they get to use the resource for the full duration of their request. Such settings are of particular significance in scientific research where large-scale instruments such as electron microscopes, particle colliders, or telescopes are shared between multiple research groups; this model also subsumes and extends existing models of repeated non-monetary allocation where resources are required for a single round only. We study a simple pseudo-market mechanism where upfront we endow each agent with a budget of artificial credits, proportional to the fair share of the resource we want the agent to receive. The endowments thus define for each agent her ideal utility as that which she derives from her favorite allocation with no competition, but subject to getting at most her fair share of the resource across rounds. Next, on each round, and for each available resource item, our mechanism runs a first-price auction with a selective reserve, wherein each agent submits a desired duration and a per-round-bid, which must be at least the reserve price if requesting for multiple rounds; the bidder with the highest per-round-bid wins, and gets to use the item for the desired duration. We consider this problem in a Bayesian setting and show that under a carefully chosen reserve price, irrespective of how others bid, each agent has a simple strategy that guarantees she receives a $1/2$ fraction of her ideal utility in expectation. We also show this result is tight, i.e., no mechanism can guarantee that all agents get more than half of their ideal utility.

翻译：我们研究非货币机制下可重用公共资源的公平高效分配问题，即资源使用时长具有可变性。考虑一个有限资源在多主体间重复共享的场景：每个主体可请求跨多个连续轮次使用该资源，仅在完整占用请求时长时获得效用。此类设置对科学研究具有特殊意义——例如电子显微镜、粒子对撞机或望远镜等大型仪器需由多个研究团队共享使用；该模型同时涵盖并扩展了现有单轮次资源需求的重复非货币分配模型。我们研究一种简洁的伪市场机制：初始阶段为每个主体分配人造积分预算，其数额与期望该主体获得的资源公平份额成比例。该初始禀赋定义了理想效用——即主体在无竞争情况下从最优分配方案中获得的效用，但需满足跨轮次资源占用不超过公平份额的约束。随后每轮次中，针对每个可用资源项目，我们的机制运行带选择性保留价的一级价格拍卖：每个主体提交期望使用时长和轮次投标价（多轮次请求时投标价须不低于保留价）；出价最高的竞标者获胜，并按期望时长占用资源。我们在贝叶斯框架下分析该问题，证明在精心设定的保留价下，无论其他主体如何投标，每个主体均可通过简单策略保证获得理想效用的1/2期望值。同时证明该结果的紧致性——即没有任何机制能确保所有主体获得超过半数理想效用。