House Allocation with Existing Tenants: An Equivalence

In this paper we analyze two house allocation mechanisms each of which is designed to eliminate inefficiencies in real-life house allocation problems where there are both existing tenants and newcomers. The first mechanism chooses the unique core allocation of a "sister" exchange economy which is constructed by assigning each existing tenant her current house and randomly assigning each newcomer a vacant house. The second mechanism -top trading cycles mechanism- first chooses an ordering from a given distribution and next determines the final outcome as follows: Assign first agent her top choice, next agent her top choice among remaining houses and so on, until someone demands house of an existing tenant who is still in the line. At that point modify the queue by inserting her at the top and proceed. Similarly, insert any existing tenant who is not already served at the top of the queue once her house is demanded. Whenever a loop of existing tenants forms, assign each of them the house she demands and proceed. Our main result is that the core based mechanism is equivalent to an extreme case of the top trading cycles mechanism which orders newcomers before the existing tenants.