Truthful mechanisms for location games of dual-role facilities

This paper is devoted to the facility location games with payments, where every agent plays a dual role of facility and customer. In this game, each selfish agent is located on a publicly known location in a metric space, and can allow a facility to be opened at his place. But the opening cost is his private information and lie may strategically report this opening cost. Besides, each agent also bears a scrvice cost equal to the distance to his nearest open facility. We are concerned with designing truthful mechanisms for the game, which, given agents' reports, output a set of agents whose facilities could be opened, and a payment to each of these agents who opens a facility. The objective is to minimize (exactly or approximately) the social cost (the total opening and service costs) or the maximum agent cost of the outcome. We characterize the normalized truthful mechanisms for this game. Concerning the minimum social-cost objective, we give an optimal truthful mechanism without regard to time complexity, and show a small gap between the best known approximation ratio of polynomial-time truthful mechanisms for the game and that of polynomial-time approximation algorithms for the counterpart of pure optimization. For the minimum maximum-cost objective, we provide an optimal truthful mechanism which runs in polynomial time. We also investigate mechanism design for the game under a budget on the total payment.