Stability and strategy-proofness for matching with constraints: A necessary and sufficient condition - Yuichiro Kamada; Fuhito Kojima (Theoretical Economics, 2018)
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: C70; D47; D61; D63; 330; Matching with constraints; medical residency matching; school choice; stability; strategy-proofness; matching with contracts; hierarchy