Enrollment manipulations in school choice

In the United States, schools with more students receive more federal funds. Yet a harsher consequence of the low enrollment is school closure. Schools, therefore, have a strong incentive to have as many students as possible. This might lead them to engage in strategic behavior to increase their enrollment. This paper studies one such kind of manipulative behavior by schools in the school choice setting. Specifically, we study whether schools can increase their enrollment levels through first concealing their capacity and then rematching for their available seats under the well-known Boston (BM), Top Trading Cycles (TTC), and stable mechanisms (Gale and Shapley, 1962). All of the mechanisms turn out to be manipulable by schools in this way whenever students can freely rematch after the centralized match. Nevertheless, if only unassigned students are allowed to rematch, then schools cannot manipulate the BM and stable mechanisms. TTC, on the other hand, continues to be manipulable.