发表机构
Ocean University of China; Laboratory of Marine Mathematics, Ocean University of China（中国海洋大学; 中国海洋大学海洋数学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对预选址设施下的设施选址博弈，设计了直线和圆周场景下、不同目标（最大成本/社会成本）及不同设置（一般/特殊）下的策略防卫机制，给出了对应的近似比与下界。
AI 中文摘要
我们研究在已预选址一个设施的前提下，为新的同质设施选址的问题。在此场景中，有n个智能体分布在直线或圆周上，每个智能体的位置为其私有信息，其成本为自身位置到最近设施的（期望）距离。我们的目标是设计机制，在能诱导智能体如实披露私有信息（即策略防卫）的同时，近似最小化最大成本或社会成本。基于现实场景，我们考虑两种设置：一般设置中每个智能体可位于预选址设施的两侧，特殊设置中所有智能体均位于预选址设施的同一侧。对于直线上的智能体，在一般设置下，我们设计了最优的确定性策略防卫机制，达到2-近似比，并针对以最大成本为目标的任意随机策略防卫机制，给出了1.5-ε（ε>0）的下界；对于社会成本，我们得到确定性策略防卫机制的上界为n，以及确定性策略防卫机制和随机策略防卫机制的下界分别为1.5和1.0425。在特殊设置下，我们进一步针对最大成本给出了随机策略防卫的5/3-近似机制，针对社会成本给出了确定性策略防卫的(n-1)-近似机制。对于圆周上的智能体，我们针对以最大成本为目标的场景，给出了确定性策略防卫的2-近似机制。
英文摘要
We study the problem of locating a new homogeneous facility under a prelocated facility. Here, a set of $n$ agents is located on a real line or a circle, each of whom has her location as private information, and her cost is the (expected) distance from her location to the nearest facility. Our goal is to design mechanisms which can approximately minimize the maximum cost or the social cost while eliciting agents' private information truthfully (i.e., strategy-proof). Based on real-life scenarios, we consider the problem in two settings: the general setting where each agent can be located at both sides of the prelocated facility, and the special setting where all the agents are located at the same side of the prelocated facility. For agents on a line, in the general setting, we design the best possible deterministic strategy-proof mechanism with $2$-approximation and provide a lower bound of $1.5-ε\textbf{ }(ε>0)$ for any randomized strategy-proof mechanism under the maximum cost objective. For the social cost, we obtain an upper bound of $n$ for deterministic strategy-proof mechanisms and lower bounds of $1.5$ and $1.0425$ for any deterministic strategy-proof mechanism and any randomized strategy-proof mechanism, respectively. In the special setting, we further provide a randomized strategy-proof $5/3$-approximation mechanism for the maximum cost and a deterministic strategy-proof $(n-1)$-approximation mechanism for the social cost. For agents on a circle, we provide a deterministic strategy-proof 2-approximation mechanism under the maximum cost objective.
