Abstract
We propose a group robust stability notion which requires robustness against a combined manipulation, fi rst misreporting preferences and then rematching, by any group of students in the school choice type of matching markets. Our first result shows that there is no group robustly stable mechanism even under acyclic priority structures (Ergin (2002)). Next, we de fine a weak version of group robust stability, called weak group robust stability. Our main theorem proves that there is a weakly group robustly stable mechanism if and only if the priority structure of schools is acyclic, and, in that case, it coincides with the student-optimal stable mechanism. Then, as a real-world practice, we add uncertainty regarding the acceptance of an appeal of a student to rematch after the announced matching. In this setting, we show that under certain conditions along with acyclicity, the student-optimal stable mechanism is group robustly stable under uncertainty.
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