On Designing Truthful Mechanisms for Online Scheduling

Abstract

We study the online version of the scheduling problem involving selfish agents considered by Archer and Tardos [FOCS 2001]: jobs must be scheduled on m parallel related machines, each of them owned by a different selfish agent.

Our study focuses on general techniques to translate approximation/competitive algorithms into equivalent approximation/competitive truthful mechanisms. Our results show that this translation is more problematic in the online setting than in the offline one.For m = 2, we develop an offline and an online “translation” technique which, given anyρ-approximation/competitive (polynomial-time) algorithm, yields an f(ρ)-approximation/competitive (polynomial-time) mechanism, with f(ρ) = ρ(1 + ε) in the offline case, for every ε > 0. By contrast, one of our lower bounds implies that, in general, online ρ-competitive algorithms cannot be turned into ρ(1 + ε)-competitive mechanisms, for some ε > 0 and every m ≥ 2.

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. Finally, we consider the variant introduced by Nisan and Ronen [STOC 1999] in which machines can be verified. For this model, we give a O(1)-competitive online mechanism for any number of machines and prove that some of the above lower bounds can be broken.

Work supported by the European Project IST-2001-33135, Critical Resource Sharing for Cooperation in Complex Systems (CRESCCO).