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。考虑一个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轮中使用该资源，且仅当获得完整时长的使用权限时才能获得效用。这类场景在科学研究中尤为重要——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团队间共享；该模型还涵盖并扩展了现有资源仅需单轮使用的重复性非货币分配模型。我们研究一种简单的伪市场机制：预先向每个智能体分配与其资源公平份额成比例的人造信用额度。该初始配给定义了每个智能体的理想效用——即无竞争状态下从最优分配方案中获得的效用，同时满足其跨轮次的资源公平份额上限。在每轮次中，针对每项可用资源，机制采用带选择性保留价的首价拍卖：每个智能体提交期望使用时长与轮次出价（若请求多轮使用，出价不得低于保留价）；最高出价者中标，并获得对应时长的资源使用权。我们在贝叶斯框架下分析该问题，证明在精心设计的保留价下，无论其他智能体如何出价，每个智能体都存在一种简单策略，可保证获得其理想效用的期望值的1/2。同时证明该结论紧致，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的一半。