We revisit the school choice problem with consent proposed by Kesten [12], which seeks to improve the efficiency of the student-optimal deferred acceptance algorithm (DA) by obtaining students' consent to give up their priorities. We observe that for students to consent, we should use their...

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...