带可选偏好和最小距离约束的真实双重厌恶型设施位置博弈
Truthful Two-Obnoxious-Facility Location Games with Optional Preferences and Minimum Distance Constraint
AI总结：
本文研究带可选偏好和最小距离约束的真实双重厌恶型设施位置博弈，提出多种确定性与随机化策略防伪机制，并给出近似比上界与下界。
摘要：
本文研究了一个真实双重厌恶型设施位置问题，其中每个智能体在[0, 1]上有一个私有位置，对两个厌恶型设施有一个公开的可选偏好，且两个设施之间存在最小距离约束d。每个智能体希望尽可能远离影响她的设施，其效用是她到这些设施的总距离。目标是决定如何在[0, 1]中放置设施，以激励智能体真实报告其私有位置，同时最大化社会效用。首先，我们考虑d = 0的特殊设定，即两个设施可位于[0, 1]中的任意点。我们分别提出了近似比至多为4的确定性策略防伪机制和近似比至多为2的随机化策略防伪机制。然后我们研究一般设定。我们分别提出了近似比至多为8的确定性策略防伪机制和近似比至多为4的随机化策略防伪机制。此外，我们分别给出了任意确定性和任意随机化策略防伪机制近似比的下界2和14/13。
英文摘要：
In this paper, we study a truthful two-obnoxious-facility location problem, in which each agent has a private location in [0, 1] and a public optional preference over two obnoxious facilities, and there is a minimum distance constraint d between the two facilities. Each agent wants to be as far away as possible from the facilities that affect her, and the utility of each agent is the total distance from her to these facilities. The goal is to decide how to place the facilities in [0, 1] so as to incentivize agents to report their private locations truthfully as well as maximize the social utility. First, we consider the special setting where d = 0, that is, the two facilities can be located at any point in [0, 1]. We propose a deterministic strategyproof mechanism with approximation ratio of at most 4 and a randomized strategyproof mechanism with approximation ratio of at most 2, respectively. Then we study the general setting. We propose a deterministic strategyproof mechanism with approximation ratio of at most 8 and a randomized strategyproof mechanism with approximation ratio of at most 4, respectively. Furthermore, we provide lower bounds of 2 and 14/13 on the approximation ratio for any deterministic and any randomized strategyproof mechanism, respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
