Agent-Constrained Truthful Facility Location Games
Argyrios Deligkas, Mohammad Lotfi, Alexandros A. Voudouris
TL;DR
This work tackles truthful facility location on a line where facilities must be placed at agent-reported locations, considering sum and max individual-cost variants. It develops and analyzes median-based mechanisms (Two-Medians, Median-Right, Median-Ball) to ensure strategyproofness and derives tight approximation bounds: for two facilities, deterministic and randomized results are provided for both variants; for general $k$, deterministic bounds are established with near-optimal gaps, and exact $k+1$ is achieved for the max-variant. The methods yield insights into how constraining candidate locations to agent reports affects social-cost efficiency and incentive compatibility, with implications for designing incentive-aware public-location decisions. The results highlight a nuanced landscape where randomized mechanisms can significantly improve performance in certain cases, while tight deterministic guarantees persist in others. Potential impact includes guiding practical placement of multiple, heterogeneous facilities under strategic reporting on real-valued domains.
Abstract
We consider a truthful facility location problem in which there is a set of agents with private locations on the line of real numbers, and the goal is to place a number of facilities at different locations chosen from the set of those reported by the agents. Given a feasible solution, each agent suffers an individual cost that is either its total distance to all facilities (sum-variant) or its distance to the farthest facility (max-variant). For both variants, we show tight bounds on the approximation ratio of strategyproof mechanisms in terms of the social cost, the total individual cost of the agents.