Before revision: We consider the problem of assigning agents to programs in the presence of two-sided preferences . Each agent has to be assigned to at most one program and each program can accommodate multiple agents. However unlike the standard setting of school choice, we do not have fixed upper quotas with programs as an input -- instead we abstract it as a cost associated with every program .
After revision: We consider the problem of assigning agents to programs in the presence of two-sided preferences , commonly known as the Hospital Residents problem. In the standard setting of school choice, we do not have fixed upper quotas with programs as an input -- instead we abstract it as a cost associated with every program .