Incentive compatibility for the stable matching model with an entrance criterion

A case study of matching students with dormitory-groups at the Technion lead recently to the study of a variant of the stable matching model with a "qualifying criterion" for the inclusion of a student among those getting an assignment. A notion of stability was introduced for the model and a (student-courting) algorithm which finds a matching that satisfied this criterion and has desired properties was described. Here, we show that students cannot benefit from misrepresenting preferences in an extension of the model that allows dormitory-groups to have different preferences over students and allows these preferences to be incomplete.