Fictitious students creation incentives in school choice problems

Abstract

We identify a new channel through which schools can potentially manipulate the well known student and school optimal stable mechanisms. We introduce two different fictitious students creation manipulation notions where one of them is stronger. While the student and school optimal stable mechanisms turn out to be weakly fictitious student-proof under acyclic (Ergin (2002)) and essentially homogeneous (Kojima (2013)) priority structures, respectively, they still lack strong fictitious student-proofness. We then compare the mechanisms in terms of their vulnerability to manipulations in the sense of Pathak and Sonmez (2013) and find out that the student-optimal stable mechanism is more manipulable than the school-optimal one. Lastly, in the large market setting of Kojima and Pathak (2009), the student-optimal stable mechanism becomes weakly fictitious student-proof as the market is getting large.