Accommodating various policy goals in matching with constraints

Distributional constraints are common features in many real matching markets, such as medical residency matching, school admissions, and teacher assignment. We present a model of matching with constraints that accommodates a wide variety of policy goals and apply that model to the setting of Kamada and Kojima (Am Econ Rev 105(1):67-99, 2015). We also formalize a number of other policy goals to show that they are subsumed by our model. We prove several comparative statics results such as showing that a mechanism we propose is a Pareto improvement for doctors upon the constrained medical matching mechanism currently used in Japan.