Market Design with Deferred Acceptance: A Recipe for Characterizations

In matching markets, policymakers often pursue complex distributional objectives, such as promoting diversity in student populations. To this end, they embed these objectives into the choice rules of institutions, such as schools, and implement the deferred-acceptance (DA) mechanism based on those rules. Given the institutional choice rules, we introduce a method for characterizing the corresponding DA mechanism through the properties of these choice rules. Utilizing this method, we derive novel characterizations of DA mechanisms across various settings, including matching problems with enrollment guarantees and overlapping reserves—motivated by school choice in Chile—as well as environments with matroidal feasibility constraints or objectives. Our approach provides a unified framework for characterizing DA mechanisms that accommodate policy-relevant objectives.