Games under the Tiered Deferred Acceptance Mechanism

We study the tiered deferred acceptance mechanism used in school admissions, such as in China and Turkey. This mechanism partitions schools into tiers and applies the deferred acceptance algorithm within each tier. Once assigned, students cannot apply to schools in subsequent tiers. We show that this mechanism is not strategy-proof. In the induced preference revelation game, we find that merging tiers preserves all equilibrium outcomes, and within-tier acyclicity is necessary and sufficient for the mechanism to implement stable matchings. We also find that introducing tiers to the deferred acceptance mechanism may not improve student quality at top-tier schools as intended.