Gradual matching with affirmative action

Abstract

This paper studies a multi-period college admissions problem where schools' choice rules incorporate affirmative action constraints. Students have the option to either finalize their assignments at the end of each period or participate in subsequent periods with the possibility of updating their rank-ordered lists (ROLs). We show that a gradual matching mechanism makes active students weakly better off (i.e. satisfies monotonicity) if and only if their ROL update rule meets a mild regularity condition. We introduce the notion of gradual stability adapted for multi-period matching mechanisms that account for affirmative action constraints. Furthermore, we show that the gradual stability of a gradual matching mechanism is equivalent to monotonicity in conjunction with the stability of the stage mechanism. Finally, we use our results to analyze the multi-stage mechanism currently used for engineering college admissions in India.