Constrained Truthful Obnoxious Two-Facility Location with Optional Preferences

TL;DR

This paper studies a truthful facility location problem on a line with agents having private positions and optional preferences over two obnoxious facilities, aiming to maximize total happiness while ensuring truthful reporting.

Contribution

It provides tight bounds on the approximation ratios of deterministic strategyproof mechanisms for both non-optional and optional preference settings.

Findings

Tight bounds for deterministic mechanisms in both settings.

Almost tight bounds for randomized mechanisms.

Mechanisms that incentivize truthful reporting while approximating optimal happiness.

Abstract

We consider a truthful facility location problem with agents that have private positions on the line of real numbers and known optional preferences over two obnoxious facilities that must be placed at locations chosen from a given set of candidate ones. Each agent wants to be as far away as possible from the facilities that affect her, and our goal is to design mechanisms that decide where to place the facilities so as to maximize the total happiness of the agents as well as provide the right incentives to them to truthfully report their positions. We consider separately the setting in which all agents are affected by both facilities (i.e., they have non-optional preferences) and the general optional setting. We show tight bounds on the approximation ratio of deterministic strategyproof mechanisms for both settings, and almost tight bounds for randomized mechanisms.