Truthful Mechanisms for Generalized Utilitarian Problems

In this paper we investigate extensions of the well-known Vickrey[1961]-Clarke[1971]Groves[1973] (VCG) mechanisms to problems whose objective function is not utilitarian and whose agents’ utilities are not quasi-linear. We provide a generalization of utilitarian problems, termed consistent problems, and prove that every consistent problem admits a truthful mechanism. These mechanisms, termed VCG-consistent mechanisms, can be seen as a natural extension of VCG mechanisms for utilitarian problems. We then investigate extensions/restrictions of consistent problems. This yields three classes of problems for which (i) VCG-consistent mechanisms are the only truthful mechanisms, (ii) no truthful VCG-consistent mechanism exists, and (iii) no truthful mechanism exists, respectively. Showing that a given problem is in one of these three classes is straightforward, thus yielding a simple way to see whether VCG-consistent mechanisms are appropriate or not. Finally, we apply our results to a number of basic non-utilitarian problems.