用于诚实单位区间覆盖的最优秩彩票
Optimal Rank Lotteries for Truthful Unit-Interval Covering
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中文总结 AI 辅助
该研究针对诚实单位区间覆盖问题，刻画了顺序统计量类彩票的最优近似比，填补了此前的近似比上下界差距，并证明了所有普遍策略防伪随机机制的近似比下界。
中文摘要 AI 辅助
在诚实区间覆盖问题中，每个智能体拥有长度为1的私有区间，目标是放置一个公共单位区间，以最小化未覆盖的总长度，同时激励智能体诚实。此前研究提出了一种基于顺序统计量机制的普遍策略防伪彩票，其近似比至多为5/3，并为该类机制建立了3/2-o(1)的下界。我们通过刻画所有基于顺序统计量的与报告无关彩票的近似比，填补了这一差距。具体而言，我们证明对于任意n≥2，该类机制的最优近似比为3/2 - 1/(2⌊n/2⌋)。除秩彩票外，我们还证明所有普遍策略防伪的随机机制的近似比至少为9/8。
英文摘要
In truthful interval covering, each agent has a private interval of unit length, and the goal is to decide where to place a public unit interval so as to minimize the total uncovered length while incentivizing the agents to be truthful. Previous work proposed a universally strategyproof lottery over order-statistic mechanisms with approximation ratio at most $5/3$, and established a lower bound of $3/2-o(1)$ for this class of mechanisms. We close this gap by characterizing the approximation ratio of every report-independent lottery over order-statistics. In particular, we show that, for every $n\ge2$, the optimal approximation ratio for this class is $\frac32-\frac{1}{2\lfloor n/2\rfloor}$. Beyond rank lotteries, we show that every universally strategyproof randomized mechanism has approximation ratio at least $9/8$.
