Random Housing with Existing Tenants

We explore the problem of distributing a group of indivisible objects, some of which incorporate a primitive assignment of use, or tenancy right. Within this framework we analyze the existence of rules always selecting an ex-ante efficient allocation, conditioned to a preservation of the tenancy rights. We realize that a probabilistic version of the Deferred Acceptance procedure (Gale and Shapley, 1962), is efficient and, from an ordinal point of view, superior to the randomized approaches of the Top Trading Cycles (Abdulkadiroglu and Sönmez, 1999) and the New House 4 mechanism employed in the MIT.