Truthful Mechanisms for Location Games of Dual-Role Facilities

This paper is devoted to the facility location games withpayments, where every agent plays a dual role of facility andcustomer. In this game, each selfish agent is located on apublicly known location in a metric space, and can allow afacility to be opened at his place. But the opening cost ishis private information and he may strategically report thisopening cost. Besides, each agent also bears a service costequal to the distance to his nearest open facility. We areconcerned with designing truthful mechanisms for the game,which, given agents’ reports, output a set of agents whosefacilities could be opened, and a payment to each of theseagents who opens a facility. The objective is to minimize(exactly or approximately) the social cost (the total openingand service costs) or the maximum agent cost of the outcome. 

We characterize the normalized truthful mechanisms forthis game. Concerning the minimum social-cost objective, wegive an optimal truthful mechanism without regard to timecomplexity, and show a small gap between the best knownapproximation ratio of polynomial-time truthful mechanismsfor the game and that of polynomial-time approximationalgorithms for the counterpart of pure optimization. For theminimum maximum-cost objective, we provide an optimaltruthful mechanism which runs in polynomial time. We alsoinvestigate mechanism design for the game under a budgeton the total payment.