Minimizing Inequity in Facility Location Games

2026-02-01

AI Summary

This work addresses intergroup unfairness arising from strategic behavior in facility location games on the real line by proposing fair mechanism designs that minimize the maximum group cost—measured either as weighted total distance or maximum distance. The study introduces two novel strategyproof mechanisms, BALANCED and MAJOR-PHANTOM, which unify classical approaches within a group fairness framework. For the single-facility setting, the authors establish tight approximation ratios; for the two-facility case, they extend endpoint-based mechanisms and prove tightness of the approximation bounds for both objectives. This research fills a theoretical gap in the analysis of approximation guarantees under group fairness criteria and substantially enhances the fairness assurances of strategyproof mechanisms in facility location problems.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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 MAJOR-PHANTOM mechanism. Both are strategyproof and achieve tight approximation guarantees under distinct formulations of the maximum group effect objective. Our mechanisms not only close the existing gap in approximation bounds for group-fairness objectives identified by Zhou, Li, and Chan (2022), but also unify many classical truthful mechanisms within a broader fairness-aware framework. For the two-facility case, we revisit and extend the classical endpoint mechanism to our generalized setting and demonstrate that it provides tight bounds for two distinct maximum group effect objectives.

Problem

• facility location
• group fairness
• inequity minimization
• strategyproofness
• max group effect

Innovation

• strategyproof mechanism
• group fairness
• facility location games
• maximum group effect
• approximation guarantee