We study non-monetary mechanisms for the fair and efficient allocation of reusable public resources. We consider settings where a limited resource is shared among a set of agents, each of whom may request to use the resource over multiple consecutive rounds, receiving some 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, and 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 some budget of artificial credits, with the budget proportion reflecting 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 items across rounds. Next, on each round, and for each available item, our mechanism runs a first-price auction with a selective reserve, wherein each agent submits a desired duration and per-round-bid (which must be at least the reserve price), and the highest bidder 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 strategy that guarantees her a $1/2$ fraction of her ideal utility in expectation. We also show this result is tight, i.e., there is no mechanism that can guarantee that all agents get more than half of their ideal utility.

翻译：我们研究了公平高效分配可复用公共资源的非货币机制。考虑有限资源在多个智能体之间共享的场景，每个智能体可请求在多个连续轮次中使用该资源，仅当完整使用整个请求时段时才能获得效用。这类场景在科学研究中具有重要意义——电子显微镜、粒子对撞机、望远镜等大型仪器需要由多个研究团队共享；该模型同时涵盖并扩展了现有仅需单轮使用资源的重复非货币分配模型。我们研究了一种简单的伪市场机制：预先向每个智能体分配一定数量的人工信用额度，其比例反映我们希望该智能体获得的资源公平份额。这种禀赋定义为每个智能体定义了其理想效用——即在无竞争条件下从最优分配中获得的效用，但受限于各轮次中获取不超过公平份额的物品数量。随后，在每一轮中，针对每个可用物品，我们的机制运行带有选择性保留价的一级价格拍卖：每个智能体提交期望使用时长和每轮出价（必须不低于保留价），出价最高者获得该物品指定时长的使用权。我们在贝叶斯框架下研究该问题，证明在精心选择的保留价下，无论其他智能体如何出价，每个智能体都存在一种策略能保证其达到期望理想效用的$1/2$。我们还证明该结果具有紧致性，即不存在任何机制能保证所有智能体获得超过其理想效用半数的收益。