Abstract In this paper, we study the problem of assigning PhD grants. Master students apply for PhD grants on different topics and the number of available grants is limited. In this problem, students have preferences over topics they applied to and the university has preferences over possible matchings of student/topic that satisfy the limited number of grants. The particularity of this framework is the uncertainty on a student’s decision to accept or reject a topic offered to him. Without using probability to model uncertainty, we study the possibility of designing protocols of exchanges between the students and the university in order to construct a matching which is as close as possible to the optimal one i.e., the best achievable matching without uncertainty