House allocation with existing tenants

Abstract

In many real-life applications of house allocation problems, whenever an existing tenant wants to move, he needs to give up his current house before getting another one. This practice discourages existing tenants from such attempts and results in loss of potentially large gains from trade. Motivated by this observation, we propose a simple mechanism that is Pareto efficient, individually rational, and strategy-proof. Our approach is constructive and we provide two algorithms, each of which can be used to find the outcome of this mechanism. One additional merit of this mechanism is that it can accommodate any hierarchy of seniorities.