On Designing Truthful Mechanisms for Online Scheduling

We study the online version of the scheduling problem Q||Cmax involving selfish agents, considered by Archer and Tardos in [FOCS 2001], where jobs must be scheduled on m related machines, each of them owned by a different selfish agent. We present a general technique for transforming competitive online algorithms for Q||Cmax into truthful online mechanisms with a small loss of competitiveness. We also investigate the issue of designing new online algorithms from scratch so to obtain efficient competitive mechanisms, and prove some lower bounds on a class of “natural” algorithms. A “direct” use of such natural algorithms to construct truthful mechanisms yields only trivial upper bounds for the case of two machines. Finally, we consider mechanisms with verification introduced by Nisan and Ronen [STOC 1999] for offline scheduling problems. We present the first constant-competitive online truthful mechanism with verification for any number of machines.