How should a group of roommates allocate the rooms and contributions to rent in the house they lease? Economists have provided partial answers to this question in a literature that spans the last 40 years. Unfortunately, these results were developed in a non-linear fashion, which obscures them to the non-specialist. Recently, computer scientists have developed an interest in this problem, advancing from an algorithmic complexity perspective. With this new interest gaining traction, there is an evident need for a coherent development of the results in economics literature. This article does so. In particular, we build connections among results that were seemingly unrelated and considerably simplify their development, fill in non-trivial gaps, and identify open questions. Our focus is on incentives issues, the area in which we believe economists have more to contribute in this discussion.
