1. then the claim follows from the strategy-proofness of DA. If i is not assigned in the first round under Qi, then the fact that i was rejected from all schools she ranks before [k]?i(Ri, Q?i) under Ri implies that these schools filled up in the first round and no seat at any of these schools can be assigned in later rounds under Qi;Consider any alternative Qi. If i is also assigned in the first round under Qi
2. The New York City high school match;A Abdulkadiro? Glu;American Economic Review,2005