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 valuations 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.