Stability and Efficiency in the General-Priority-Based Assignment

Abstract

We introduce a general class of priority orders over sets, which captures both indifferences and substitutability. Our notion of substitutability ensures the existence of stable assignment. The characterization of efficient priority structures implies that there is usually a conflict between efficiency and stability. Thus we turn to the problem of finding a constrained efficient assignment, and give an algorithm which solves the problem for any priority structure that falls into our class. As an important application, gender equality or racial equality in school choice can be captured by our model, but not previous models in the literature.