Strategy-proof school choice mechanisms with minimum quotas and initial endowments.

We consider a school choice program where minimum quotas are imposed for each school, i.e., a school must be assigned at least a certain number of students to operate. We require that the obtained matching must respect the initial endowments, i.e., each student must be assigned to a school that is at least as good as her initial endowment school. Although minimum quotas are relevant in school choice programs and strategy-proofness is important to many policymakers, few existing mechanisms simultaneously achieve both. One difficulty is that no strategy-proof mechanism exists that is both efficient and fair under the presence of minimum quotas. Furthermore, existing mechanisms require that all students consider all schools acceptable to obtain a feasible matching that respects minimum quotas. This assumption is unrealistic in a school choice program.