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：我们研究用于公平高效分配可重用公共资源（即使用时长可变的资源）的非货币机制。考虑有限资源在多个智能体之间重复共享的场景，每个智能体可请求在连续多个轮次中使用资源，仅当完整使用所请求持续时间时才能获得效用。这类场景在科学研究中尤为重要，例如电子显微镜、粒子对撞机或望远镜等大型设备需在多个研究组之间共享；该模型同时涵盖并扩展了现有单轮次资源分配的非货币重复分配模型。我们提出一种简单伪市场机制：首先为每个智能体分配与资源公平份额成比例的人工信用额度，该额度定义了智能体在无竞争情况下获取最优分配的理想效用，但受限于跨轮次获得不超过公平份额的资源量。随后在每轮次中，对于每个可用资源项，机制执行含选择性保留价的一级价格拍卖：智能体提交期望使用时长和轮次竞价，多轮次请求时竞价需不低于保留价；出价最高的竞拍者胜出并获得相应时长的资源使用权。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，无论其他智能体如何报价，每个智能体都存在简单策略使其可获得期望理想效用的$1/2$分数。同时证明该结果紧致，即不存在能保证所有智能体获得超过半理想效用的机制。