Stable and Efficient Resource Allocation with Contracts

Consider indivisible-object allocation with contracts, such as college admissions, where contracts specify majors. Can a designer guarantee a stable and (student) efficient matching? I show that contracts put stability and efficiency at odds; a necessary condition to ensure these properties is student-lexicographic priorities—schools must rank contracts from “second-tier” students consecutively. I present the weakest restriction guaranteeing stability and efficiency, and characterize necessary and sufficient conditions for any mechanism within a general class to deliver a stable and efficient matching in an incentive compatible manner. I apply this result to two well-known mechanisms: deferred acceptance and top trading cycles. (JEL C78, D82, D86, I23)