College admissions with affirmative action

Abstract

This paper first shows that when colleges' preferences are substitutable there does not exist any stable matching mechanism that makes truthful revelation of preferences a dominant strategy for every student. The paper introduces student types and captures colleges' preferences for affirmative action via type-specific quotas: A college always prefers a set of students that respects its type-specific quotas to another set that violates them. Then it shows that the student-applying deferred acceptance mechanism makes truthful revelation of preferences a dominant strategy for every student if each college's preferences satisfy responsiveness over acceptable sets of students that respect its type-specific quotas. These results have direct policy implications in several entry-level labor markets (Roth 1991). Furthermore, a fairness notion and the related incentive theory developed here is applied to controlled choice in the context of public school choice by Abdulkadiroğlu and Sönmez (2003).