This paper develops a price-theoretic framework for matching markets with heterogeneous preferences. The model departs from the standard Gale and Shapley (1962) model by assuming that a finite number of agents on one side (colleges or firms) are matched to a continuum mass of agents on the other...

In matching markets, the existence of stable matchings can only be guaranteed under substantive restrictions on preferences. We investigate how these results change in large markets, which we model with a continuum of agents of each type, following the work of Aumann (1964) on general...

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...