Isa E. Hafalir, Fuhito Kojima, M. Bumin Yenmez
Given an initialmatching and a policy objective on the distribution of agent types to institutions, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual rationality, and strategy-proofness. We show that such a mechanism need not exist in general. We introduce a new notion of discrete concavity, which we call pseudo M♮-concavity, and construct a mechanismwith the desirable properties when the distributional objective satisfies this notion. We provide several practically relevant distributional objectives that are pseudo M♮-concave.