 In this paper , we explore the problem of finding a stable many-to-one matching  while satisfying fairness among the agents , having cardinal utilities.
<meaning-changed>  In this paper , we explore the problem of finding a stable many-to-one matching  while satisfying fairness among the agents , having cardinal utilities.
 In this paper , we explore the problem of finding a stable many-to-one matching , under cardinal valuations, while satisfying fairness among the agents , having cardinal utilities.