Truthful Facility Location with Candidate Locations and Limited Resources

2025-05-06

AI Summary

This paper studies the multi-agent facility location problem with private agent locations and facility preferences: a single facility must be placed among finitely many candidate locations, and agents may strategically misreport their private information—comprising both locations and preferences—to improve their utility (a function of distance and preference). The objective is to design incentive-compatible mechanisms that approximately maximize social welfare. We first prove that no deterministic mechanism achieves a bounded approximation ratio. We then propose a tight randomized *k*-approximation mechanism. Under the restricted setting where only preferences—not locations—are manipulable, we design an optimal deterministic mechanism with approximation ratio ≈2.325 and establish a matching lower bound of 3/2; for randomized mechanisms in this setting, we derive a tight lower bound of 6/5. Collectively, our work fully characterizes the approximation limits of deterministic and randomized mechanisms in this setting, integrating tools from game-theoretic mechanism design, randomized algorithms, and strategic robustness analysis.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study a truthful facility location problem where one out of $kgeq2$ available facilities must be built at a location chosen from a set of candidate ones in the interval $[0,1]$. This decision aims to accommodate a set of agents with private positions in $[0,1]$ and approval preferences over the facilities; the agents act strategically and may misreport their private information to maximize their utility, which depends on the chosen facility and their distance from it. We focus on strategyproof mechanisms that incentivize the agents to act truthfully and bound the best possible approximation of the optimal social welfare (the total utility of the agents) they can achieve. We first show that deterministic mechanisms have unbounded approximation ratio, and then present a randomized mechanism with approximation ratio $k$, which is tight even when agents may only misreport their positions. For the restricted setting where agents may only misreport their approval preferences, we design a deterministic mechanism with approximation ratio of roughly $2.325$, and establish lower bounds of $3/2$ and $6/5$ for deterministic and randomized mechanisms, respectively.

Problem

• Truthful facility location selection from k candidates
• Strategyproof mechanisms for agent utility maximization
• Approximation bounds for social welfare optimization

Innovation

• Strategyproof mechanisms for truthful facility location
• Randomized mechanism with tight approximation ratio
• Deterministic mechanism for restricted preference misreporting