Details for Talk on: 21.11.2016

We investigate first choice-maximality (FCM) (i.e., a maximal share of students is matched to their reported first choices), a common desideratum in the design of school choice mechanisms. No FCM mechanism can be stable; however, we find first choice-stability (FCS) (i.e., no student forms a blocking pair with her first choice) to be the strongest rank-based relaxation of stability that is compatible with FCM. Focusing on the class of FCM and FCS mechanisms (which includes the widely used Boston mechanism), we show that the Pareto efficient members of this class form a minimally manipulable subset. Moreover, we identify the Nash equilibrium outcomes of any mechanism in this class when all students are strategic and when some student are sincere. Our analysis generalizes that of Ergin and Sönmez (2006) and Pathak and Sönmez (2008) from the Boston mechanism to the general class of FCM and FCS mechanisms. Our results suggest a novel approach to the design of school choice mechanisms where strategic students self-select into receiving their reported school in a first step, so that in a second step, the matching of sincere students can be made independently of the usual incentive constraints