Abstract
We address the question of whether schools can manipulate the student-optimal stable mechanism by creating fictitious students in school choice problems. To this end, we introduce two different manipulation concepts, where one of them is stronger. Our first result demonstrates that the student-optimal stable mechanism is not strongly fictitious student-proof even under acyclic priority structures (Ergin (2002)). Then, for the weak one, our main theorem shows that the student-optimal stable mechanism is weakly fictitious student-proof if and only if the priority structure of schools is acyclic.
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