Truthful Facility Location with Candidate Locations and Limited Resources

TL;DR

This paper investigates strategyproof mechanisms for a facility location problem with candidate sites and limited resources, providing bounds on social welfare approximation for both deterministic and randomized approaches.

Contribution

It introduces new mechanisms for truthful facility location with approximation bounds, including a tight randomized mechanism and bounds for restricted misreporting.

Findings

Randomized mechanism achieves approximation ratio of k, tight for general agents.

Deterministic mechanisms have unbounded approximation ratio.

New deterministic and randomized mechanisms with specific approximation ratios for restricted agent misreports.

Abstract

We study a truthful facility location problem where one out of $k\geq2$ 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.