We study the trade-off between stability and students' welfare in school choice problems. We call a matching weakly stable if none of its blocking pairs can be matched in a more stable matching–one with a weakly smaller set of blocking pairs. A matching is said to be self-constrained efficient...

We propose a notion of core for school choice problems. We say that a coalition of students is able to enforce a subassignment among them if, given their priorities at schools, other students together cannot exclude any of them from her assignment. An assignment is in the core if no coalition of...