Mechanism design with partial verification and revelation principle

In the case of mechanism design with partial verification, where agents have restrictions on misreporting, the Revelation Principle does not always hold. Auletta et al. (J Auton Agent Multi-Agent Syst, to appear) proposed a characterization of correspondences for which the Revelation Principle holds, i.e., they described restrictions on misreporting under which a social choice function is implementable if and only if it is truthfully implementable. In this paper, we demonstrate that the characterization proposed in [1] is incorrect, and, building on their work, give a correct characterization. We also provide an example that demonstrates that our characterization is different from that of Auletta et al.