Strategic Facility Location with Limited Liars

2026-04-18

AI Summary

This study addresses metric facility location games with $k$ strategic agents who may misreport their locations to gain individual advantage, thereby degrading system efficiency. For the first time, it quantifies the impact of a limited number of strategic users on equilibrium quality by integrating game-theoretic analysis, approximation algorithms, and metric space properties. The authors prove that a Nash equilibrium always exists and exhibits near-optimal price of stability, with a tight upper bound on the price of anarchy given by $(n+2k)/(n-2k)$. Furthermore, under linear metrics, a strong equilibrium is guaranteed to exist, achieving an approximation ratio of at most $(n+k)/(n-k)$. These results demonstrate that even when $k$ is relatively large, equilibrium performance remains substantially superior to that of fully strategyproof mechanisms.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Search and Optimization: Combinatorial Optimization

Application Category

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

Abstract

We study Nash equilibria in strategic facility location games where clients are located in an arbitrary metric space. Specifically, there are $n$ clients, and the goal is to choose a facility from a set of given locations, so that the total distance from the clients to the facility is as small as possible. While some of the clients are always truthful, $k$ of them are strategic, and will lie about their location if it benefits them. We quantify how the fraction of strategic clients affects the existence and quality of Nash equilibrium and strong equilibrium solutions, and note that even for relatively large $k$, the properties of these solutions can be much better than the results of fully strategyproof mechanisms. For Nash equilibrium, we show that it always exists, and the price of stability is very close to 1. More importantly, we prove that all Nash equilibria are within a factor of at most $\frac{n+2k}{n-2k}$ from the optimum solution, and that this price of anarchy bound is almost tight. While strong equilibrium may not exist for this setting, we prove that it always exists for line metrics, and its cost is at most $\frac{n+k}{n-k}$ times that of optimum.

Problem

• Facility Location
• Strategic Agents
• Nash Equilibrium
• Price of Anarchy
• Metric Space

Innovation

• strategic facility location
• limited liars
• Nash equilibrium
• price of anarchy
• strong equilibrium