In the many-to-one matching model with contracts, I show that there is no restriction on preferences weaker than substitutable preferences which guarantees that the set of stable allocations is a lattice. Thus, when contracts are not substitutes, removing agents from the economy may decrease the...

In an attempt to increase the placement of medical residents to rural hospitals, the Japanese government recently introduced "regional caps" which restrict the total number of residents matched within each region of the country. The government modified the deferred acceptance mechanism...