Eduardo Duque Rosas

The student-optimal stable mechanism (DA), the most popular mechanism in school choice, is the only one that is both stable and strategy-proof. However, when DA is implemented, a student can change the schools of others without changing her own. We show that this drawback is limited: a student cannot change her classmates without modifying her school. We refer to this new property as local non-bossiness. Along with strategy-proofness, it ensures a local notion of group strategy-proofness in which manipulating coalitions are restricted to students in the same school. Furthermore, local non-bossiness plays a crucial role in incentives when students have preferences over their colleagues.

In classical school choice contexts there exists a centralized assignment procedure that is stable and strategy-proof: the Gale-Shapley student-optimal stable mechanism. We show that this property is not satisfied when externalities are incorporated into the model, even in scenarios in which students are primarily concerned about their own placement. Indeed, although weak externalities have no effects on stability, there are school choice contexts in which no stable and strategy-proof mechanism exists. Furthermore, we show that stability and strategy-proofness are compatible if and only if schools' priorities are Ergin-acyclic.