Fictitious students creation incentives in school choice problems

We identify a new channel through which schools can potentially manipulate the well-known student and school-optimal stable mechanisms. We introduce two 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 in Econometrica 88:485–494, 2002) and essentially homogeneous (Kojima in Games Econ Behav 82:1–14, 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 Sönmez (Am Econ Rev 103(1):80–106, 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 (Am Econ Rev 99(3):608–627, 2009), the student-optimal stable mechanism becomes weakly fictitious student-proof as the market is getting large.