Facility Location Games with Ordinal Preferences

TL;DR

This paper studies strategyproof mechanisms for facility location games with agents having ordinal preferences, providing bounds on approximation ratios for various objectives and settings, and exploring generalizations beyond two facilities.

Contribution

It introduces a new setting with ordinal preferences, analyzes strategyproof mechanisms for multiple objectives, and establishes tight bounds for two-facility scenarios with private preferences or locations.

Findings

Derived lower and upper bounds on approximation ratios for different objectives.

Established asymptotic tightness of bounds up to a constant.

Extended analysis to scenarios with more than two facilities and combined misreporting.

Abstract

We consider a new setting of facility location games with ordinal preferences. In such a setting, we have a set of agents and a set of facilities. Each agent is located on a line and has an ordinal preference over the facilities. Our goal is to design strategyproof mechanisms that elicit truthful information (preferences and/or locations) from the agents and locate the facilities to minimize both maximum and total cost objectives as well as to maximize both minimum and total utility objectives. For the four possible objectives, we consider the 2-facility settings in which only preferences are private, or locations are private. For each possible combination of the objectives and settings, we provide lower and upper bounds on the approximation ratios of strategyproof mechanisms, which are asymptotically tight up to a constant. Finally, we discuss the generalization of our results beyond two facilities and when the agents can misreport both locations and preferences.