Strategy proofness and unanimity in many-to-one matching markets

In this paper, we consider a standard model of many-to-one matching markets. First, we study the relation between strategy-proofness and unanimity under a certain requirement and we prove these two properties become equivalent. Second, we illustrate that this result has an immediate impact on the relation between strategy-proofness and Maskin monotonicity. Finally, we determine a close connexion between strategy-proofness and implementation literature. We provide under certain minimal requirements the foundation for reasoning the equivalence among dominant strategy implementation, standard Nash implementation, and partially honest Nash implementation.