We introduce a generalization of the school choice problem motivated by the following observations: students are assigned to grades within schools, many students have siblings who are applying as well, and school districts commonly guarantee that siblings will attend the same school. This last...

We introduce a generalization of the school choice problem motivated by the following observations: students are assigned to grades within schools, many students have siblings who are applying as well, and school districts commonly guarantee that siblings will attend the same school. This last...

We explore the possibility of designing matching mechanisms that can accommodate non-standard choice behavior. We pin down the necessary and sufficient conditions on participants’ choice behavior for the existence of stable and incentive compatible mechanisms. Our results imply that...