Mechanisms with Verification for Any Finite Domain

Abstract

In this work we study mechanisms with verification, as introduced by Nisan and Ronen [STOC 1999], to solve problems involving selfish agents. We provide a technique for designing truthful mechanisms with verification that optimally solve the underlying optimization problem. Problems (optimally) solved with our technique belong to a rich class that includes, as special cases, utilitarian problems and many others considered in literature for so called one-parameter agents (e.g., the make-span). Our technique extends the one recently presented by Auletta et al [ICALP 2006] as it works for any finite multi-dimensional valuation domain. As special case we obtain an alternative technique to optimally solve (though not in polynomial-time) Scheduling Unrelated Machines studied (and solved) by Nisan and Ronen. Interestingly enough, our technique also solves the case of compound agents (i.e., agents declaring more than a value). As an application we provide the first optimal truthful mechanism with verification for Scheduling Unrelated Machines in which every selfish agent controls more than one (unrelated) machine. We also provide methods leading to approximate solutions obtained with polynomial-time truthful mechanisms with verification. With such methods we obtain polynomial-time truthful mechanisms with verification for smooth problems involving compound agents composed by one-parameter valuations. Finally, we investigate the construction of mechanisms (with verification) for infinite domains. We show that existing techniques to obtain truthful mechanisms (for the case in which verification is not allowed), dealing with infinite domains, could completely annul advantages that verification implies.

Research partially supported by the European Project FP6-15964, Algorithmic Principles for Building Efficient Overlay Computers (AEOLUS).