Facility Location Game with Envy Ratio

2026-07-02

AI Summary

This study introduces the notion of envy-freeness into single-facility location games on the real line and investigates strategyproof mechanism design under two constrained settings: (1) both agents and the facility are restricted to a fixed interval, and (2) agents may be located arbitrarily while the facility is confined to a relative interval. Drawing upon mechanism design theory, game theory, and optimization techniques, the authors construct both deterministic and randomized strategyproof mechanisms and establish their respective lower bounds. The main contributions include optimal deterministic group-strategyproof mechanisms for both settings; for randomized mechanisms, a tight lower bound in the first setting and a lower bound accompanied by two upper bounds in the second setting, thereby providing a theoretical foundation and mechanistic guarantees for fair facility location.

Abstract

We study the one-facility location game on a real line with a new objective called envy ratio. The envy ratio, which is adopted from fair division and represents the egalitarianism, is defined as the maximum over the ratios between any two agents' utilities. We are interested in strategyproof or group strategyproof mechanisms that can minimize the envy ratio objective. We consider the model in two settings that can capture natural scenarios: the facility location and all the agents' locations are restricted on a fixed interval; every agent's location can be any point on the real line but the facility location is restricted on a relative interval. In both settings, we obtain the optimal solution and the best deterministic strategyproof mechanism which is also group strategyproof. In the first setting, we provide a lower bound for randomized strategyproof mechanisms. In the second setting, we give a lower bound and two upper bounds for randomized strategyproof mechanisms.

Problem

• Facility Location
• Envy Ratio
• Strategyproofness
• Fair Division
• Mechanism Design

Innovation

• envy ratio
• facility location game
• strategyproof mechanism
• group strategyproofness
• fair division