Before revision:  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 . This setting enables the programs to control the number of agents assigned to them and is also applicable in the two-round setting (Gajulapalli et al. , FSTTCS 2020) where largest stable extension is computed. In this setting, our goal is to compute a min-cost stable matching that matches all the agents .
After revision:  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 and these costs control the quotas. Our goal is to compute a min-cost stable matching that matches all the agents .