We initiate the study of a novel problem in mechanism design without money, which we term Truthful Interval Covering (TIC). An instance of TIC consists of a set of agents each associated with an individual interval on a line, and the objective is to decide where to place a covering interval to minimize the total social cost of the agents, which is determined by the intersection of this interval with their individual ones. This fundamental problem can model situations of provisioning a public good, such as the use of power generators to prevent or mitigate load shedding in developing countries. In the strategic version of the problem, the agents wish to minimize their individual costs, and might misreport the position and/or length of their intervals to achieve that. Our goal is to design truthful mechanisms to prevent such strategic misreports and achieve good approximations to the best possible social cost. We consider the fundamental setting of known intervals with equal lengths and provide tight bounds on the approximation ratios achieved by truthful deterministic mechanisms. We also design a randomized truthful mechanism that outperforms all possible deterministic ones. Finally, we highlight a plethora of natural extensions of our model for future work, as well as some natural limitations of those settings.

翻译：本文首次研究无货币机制设计中的一个新问题，我们称之为"真实区间覆盖"(Truthful Interval Covering, TIC)。TIC问题包含一组代理，每个代理关联一条直线上的个人区间，目标是确定覆盖区间的放置位置，以最小化代理的总社会成本——该成本由覆盖区间与个人区间的交集长度决定。这一基础问题可建模公共物品供给场景，例如通过使用发电机来预防或缓解发展中国家的负荷削减。在该问题的策略性版本中，代理旨在最小化自身成本，可能虚报其区间的长度和/或位置。我们的目标是设计真实机制以防止此类策略性虚报行为，并实现尽可能接近最优社会成本的近似比。针对已知等长区间的基本设定，我们给出了确定性真实机制所能达到的近似比紧界，并设计了一种随机化真实机制，其性能优于所有可能的确定性机制。最后，我们指出模型中大量值得在未来工作中探讨的自然扩展情形，并阐明这些设定存在的固有局限性。