Before revision:  In the special case of ranked utilities where all agents on each side have the same  rankings over the agents on the other side (but not necessarily the same utilities) , we provide a characterisation for the space of stable matchings.
After revision:  In the special case of ranked utilities where all agents on each side have the same rankings over the agents on the other side (but not necessarily the same valuations). For this special case , we provide a characterisation for the space of stable matchings.