Monotonicity Implies Strategy-Proofness for Correspondences

We show that Maskin monotone social choice correspondences on sufficiently rich domains satisfy a generalized strategy-proofness property, thus generalizing Muller and Satterthwaite's (1977) theorem to correspondences. From the point of view of Nash implementation theory, the result yields a partial characterization of the restrictions entailed by Nash implementability. Alternatively, the result can be viewed as a possibility theorem on the dominant-strategyimplementability of monotone SCCs via set-valued mechanisms for agents who are completely ignorant about the finally selected outcome. It is shown by examples that stronger strategy-proofness properties fail easily.