Facility location games with ordinal preferences

In this paper we study a novel model of facility location games with ordinal preferences. There is a set of self-interested agents and a set of heterogeneous 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 true 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. Furthermore, we extend some of the results to the multiple-facility setting. Finally, we discuss the generalization of our results when the agents can misreport both locations and preferences, and the case when the approximations are defined additively.