A Many-to-Many ‘Rural Hospital Theorem’

• Authors: Flip Klijn.
• BSE Working Paper: 110056 | September 15
• Keywords: stability , matching , many-to-many , rural hospital theorem
• JEL codes: C78, D60
• stability
• matching
• many-to-many
• rural hospital theorem

We show that the full version of the so-called “rural hospital theorem” generalizes to many-to-many matching problems where agents on both sides of the problem have substitutable and weakly separable preferences. We reinforce our result by showing that when agents’ preferences satisfy substitutability, the domain of weakly separable preferences is also maximal for the rural hospital theorem to hold.