Theoretical Economics 13 (2018), 761–794

Distributional constraints are common features in many real matching markets, such as medical residency matching, school admissions, and teacher assignment. We develop a general theory of matching mechanisms under distributional constraints. We identify the necessary and sufficient condition on the constraint structure for the existence of a mechanism that is stable and strategy-proof for the individuals. Our proof exploits a connection between a matching problem under distributional constraints and a matching problem with contracts.

Keywords: Matching with constraints, medical residency matching, school choice, stability, strategy-proofness, matching with contracts, hierarchy

JEL classification: C70, D47, D61, D63