Discussion Paper Series College Admissions with Affirmative Action

Abstrac t 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. It introduces student types and captures colleges ' prefer-ences towards affirmative action via type specific quotas: A college always prefers a set of students that respects its type specific quo-tas to another set that violates them. Then it shows that a stable mechanism that makes truthful revelation of preferences a dominant strategy for every student exists if and only 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, the al-gorithm and the related incentive theory developed here is applied to controlled choice in the context of public school choice by Abdulka-diroglu and Sonmez (2003).