Some Technical Results on Continuity , Strategy - proofness , and Related Strategic

There are many concepts of nonmanipulability, including strategy-proofness (and its several coalitional variants), Nash implementability, self Nash implementability, and nonbossi-ness. We explore the relationships between these concepts in the context of continuous social choice functions (SCF's). For any continuous SCF on a continuously and monotonically closed domain, we nd that strategy-proofness implies strict strategy-proofness, and that strategy-proofness and nonbossiness imply Maskin monotonicity. On the domain of mono-tonic, nonlocally satiated, and strictly convex preferences over < m + , any strictly strategy-proof SCF is continuous, and any continuous, strategy-proof, and nonbossy SCF is strictly coalitionally strategy-proof. On the domain of monotonic, nonlocally satiated, and convex preferences over < m + , any coalitionally strategy-proof SCF is Maskin monotonic, and any strategy-proof and nonbossy social choice function is completely characterized by its values on the set of linear preferences. 1 I gratefully acknowledge many helpful discussions with Herv e Moulin.