Truthful Combinatorial Assignment without Money

Mechanism design with agents who do not have quasi-linear preferences is an important line of research in social choice theory. Finding domains which admit truthful mechanisms is of central importance, particularly due to the well known impossibility result by Gibbard and Satterthwaite. In this paper we introduce a general framework for combinatorial assignments without money but with public valuations and explore the possibility of truthful mechanism design within this model. We show truthful mechanisms as well as impossibility results for restricted settings. For the general setting, we propose a randomized truthful mechanism. Finally, we analyze a strategic variant of the generalized assignment problem where every machine is owned by a selfish agent who aims to maximize the value of her own assignment. For variants of this problem we propose truthful mechanisms.