在设施选址游戏中最小化不平等
Minimizing Inequity in Facility Location Games
AI总结：
本文提出两种新的机制以最小化设施选址游戏中群体效应，统一了多个经典诚实机制，并改进了群体公平目标的近似界限。
摘要：
本文研究了在实线上设施选址游戏中最小化群体层面不平等的问题，其中代理属于不同群体且可能采取策略性行为。我们探索了一个以公平为导向的目标，该目标最小化Marsh和Schilling（1994）引入的最大群体效应。每个群体的效应定义为其到最近设施的总距离或最大距离，按群体特定因素加权。我们证明了这种形式化涵盖了多个著名的优化目标，包括经典的功利主义（社会成本）和平等主义（最大成本）目标，以及两个群体公平目标，最大总成本和平均群体成本。为了最小化最大群体效应，我们首先提出了两种新的机制用于单设施情况，即BALANCED机制和MAJOR-PHANTOM机制。两者都是策略证明的，并在不同的最大群体效应目标形式化下实现了紧致的近似保证。我们的机制不仅填补了Zhou、Li和Chan（2022）所识别的群体公平目标近似界限的现有差距，还将在更广泛的公平意识框架内统一了许多经典的诚实机制。对于双设施情况，我们回顾并扩展了经典的端点机制到我们的通用设置，并展示了它为两种不同的最大群体效应目标提供了紧致的界限。
英文摘要：
This paper studies the problem of minimizing group-level inequity in facility location games on the real line, where agents belong to different groups and may act strategically. We explore a fairness-oriented objective that minimizes the maximum group effect introduced by Marsh and Schilling (1994). Each group's effect is defined as its total or maximum distance to the nearest facility, weighted by group-specific factors. We show that this formulation generalizes several prominent optimization objectives, including the classical utilitarian (social cost) and egalitarian (maximum cost) objectives, as well as two group-fair objectives, maximum total and average group cost. In order to minimize the maximum group effect, we first propose two novel mechanisms for the single-facility case, the BALANCED mechanism and the MajorPhantom mechanism. Both are strategyproof and achieve tight approximation guarantees under distinct formulations of the maximum group effect objective. Our mechanisms recover the known tight approximation guarantees for classical group-fair objectives as special cases, while extending them to a broader weighted framework and unifying several classical truthful mechanisms.
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