Monotonicity implies generalized strategy-proofness for correspondences

Abstract.

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. The result is interpreted as a possibility theorem on the dominant-strategy implementability of monotone SCCs via set-valued mechanisms for agents who are completely ignorant about the finally selected outcome. Alternatively, the result yields a partial characterization of the restrictions entailed by Nash implementability of correspondences.