Truthful Mechanisms for Generalized Utilitarian Problems

Abstract

In this paper we investigate extensions of the well-known Vickrey-Clarke-Groves (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 VCGconsistent (VCGc) 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) VCGc mechanisms are the only truthful mechanisms, (ii) no truthful VCGc 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 VCGc mechanisms are appropriate or not.Finally, we apply our results to a number of basic non-utilitarian problems.

A truthful mechanism for the non-utilitarian minimum radius spanning tree problem

“…, a k } the set of agents, and let us assume that no agent is indispensable, in the sense that for any agent, the removal of all the components belonging to this agent leaves the set of feasible solutions nonempty for the problem we are solving. This is a crucial property to guarantee the existence of truthful mechanisms [11]. With V (a i ) and E(a i ) we denote the set of nodes and the set of edges owned by any a i ∈ A, respectively.…”