On Two Competing Affirmative Actions under Deferred Acceptance Algorithm

In this paper, we study two kinds of affirmative action policies, quota-based and reserve-based, under the Gale-Shapley student-optimal stable mechanism (SOSM). We first try to reveal the source of perverse affirmative action policies, especially on the purported beneficiaries. We show that a variant of Ergin-acyclicity structure, type-specific acyclicity, is crucial for effective affirmative action policies. This result may provide a simple criterion to decide whether affirmative action is appropriate to implement under certain market structure. We next include college's incentive into consideration, and indicate that for all markets without type-specific cycles and with sufficient competition for each unfilled seat, the reserve-based affirmative action is more vulnerable to manipulation compare to its quota-based counterpart. This argument implies that the efficiency gain from the more flexible reserve-based policy may be offset by its vulnerability to manipulation. Under some regularity conditions, we demonstrate that truthful reporting by every participant is an approximate equilibrium when the number of colleges is sufficiently large.