Characterization of Truthful Mechanisms for One-Dimensional Single Facility Location Game with Payments

Abstract

In a one-dimensional single facility location game, each player resides at a point on a straight line his location; the task is to decide the location of a single public facility on the line. Each player derives a nonnegative cost, which is a monotonically increasing function of the distance between the location of the facility and himself, so he may misreport his location to minimize his cost. It is desirable to design an incentive compatible allocation mechanism, in which no player has an incentive to misreport. Offering/Charging payments to players is a usual tool for a mechanism to adjust incentives. Our game setting without payment is equivalent to the voting setting where voters have single-peaked preferences. A complete parametric characterization of incentive compatible allocation mechanisms in this setting was given by [17], while the problem for games with payments is left open. We give a characterization for the case of linear and strictly convex cost functions by showing the sufficiency of weak-monotonicity, which, more importantly, implies an interesting monotone triangular structure on every single-player subfunction.