In classical school choice problems there always exist a mechanism that is stable, strategy-proof, and weakly Pareto efficient: the Gale-Shapley student-optimal stable mechanism. This situation drastically changes when externalities are incorporated into the model. Indeed, even when students are primarily concerned about their own placement, there are school choice contexts in which no stable mechanism is either strategy-proof or weakly Pareto efficient. Furthermore, stability and strategy-proofness are compatible if and only if schools' priorities are Ergin-acyclic. This strong effect of weak externalities on incentives is related to the incompatibility between stability, strategy-proofness, and non-bossiness in school choice problems without externalities.
Eduardo Duque, Universidad de los Andes, Chile
Juan Pablo Torres-Martínez, Universidad de Chile