Equitable Mechanism Design for Facility Location

2025-06-12

AI Summary

This paper studies strategy-proof mechanism design for facility location problems, aiming to enhance fairness in user utility allocation. Recognizing the fundamental inapproximability of Gini index optimization, the authors introduce the *complementary Gini index* as a unified fairness criterion compatible with both deterministic and randomized mechanisms. Leveraging tools from mechanism design, social choice theory, and approximation analysis, they establish tight approximation bounds for strategy-proof mechanisms under fairness constraints: they derive optimal approximation ratios for both deterministic and randomized mechanisms with respect to the complementary Gini index, and quantify their guaranteed Nash welfare. The results provide a theoretical foundation and design paradigm for jointly optimizing fairness and strategy-proofness in facility location.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

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

Abstract

We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarian and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.

Problem

• Strategy-proof mechanisms for equitable facility location
• Approximation ratios for complemented Gini index
• Mechanisms' performance in approximating Nash welfare

Innovation

• Strategy proof mechanisms for facility location
• Approximation ratios of complemented Gini index
• Mechanisms approximating Nash welfare equitably