发表机构
University of Nebraska-Lincoln; Rensselaer Polytechnic Institute; Beijing Normal University-Zhuhai（内布拉斯加大学林肯分校; 伦斯勒理工学院; 北京师范大学珠海校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种奇偶依赖的随机化机制，混合随机独裁者与比例圆距离机制，在圆上战略设施选址中实现策略证明且近似比为3/2，并改进下界至11/10。
AI 中文摘要
我们研究在功利主义社会成本目标下，在圆上定位单一设施以服务一组战略智能体的策略证明机制。我们分析了一种简单的奇偶依赖机制，该机制在随机独裁者（RD）机制和比例圆距离（PCD）机制之间进行随机化。对于奇数个智能体 $n$，该机制以相等概率混合 RD 和 PCD，正如 Rogowski 和 Dziubiński（IJCAI 2025）最初提出的那样。对于偶数 $n$，它将 RD 与 PCD 的随机删除扩展混合，在该扩展中，在将 PCD 应用于剩余智能体之前，均匀随机地移除一个智能体。我们的主要结果表明，该机制是策略证明的，并且对于每个 $n\ge 3$ 都实现了 $\frac32$ 的近似比。这改进了 Rogowski 和 Dziubiński 仅适用于奇数 $n$ 的 $\frac74$ 上界，并将保证扩展到偶数个智能体。最后，我们建立了任何随机化策略证明机制的近似比的下界为 $\frac{11}{10}$，改进了 Meir（SAGT 2019）之前的 $1.0456$ 下界。
英文摘要
We study strategyproof mechanisms for locating a single facility on a circle so as to serve a set of strategic agents under the utilitarian social cost objective. We analyze a simple parity-dependent mechanism that randomizes between the Random Dictator (RD) mechanism and the Proportional Circle Distance (PCD) mechanism. For an odd number \(n\) of agents, this mechanism mixes RD and PCD with equal probability, as originally proposed by Rogowski and Dziubi{ń}ski (IJCAI 2025). For even \(n\), it mixes RD with a random-deletion extension of PCD, in which one agent is removed uniformly at random before PCD is applied to the remaining agents. Our main result shows that this mechanism is strategyproof and achieves an approximation ratio of \(\frac32\) for every \(n\ge 3\). This improves the \(\frac74\) upper bound of Rogowski and Dziubi{ń}ski, which applied only to odd \(n\), and extends the guarantee to even numbers of agents. Finally, we establish a computer-assisted lower bound of \(1.088187\ldots\) on the approximation ratio of any randomized strategyproof mechanism, improving on the previous lower bound of \(1.0456\) due to Meir (SAGT 2019).
Commentsv1 is finished in June 2026, and v2 is revised with the assistance of GPT Astra-6
