Mutually best matches

We study iterated formation of mutually best matches (IMB) in college admissions problems. When IMB produces a non-wasteful matching, the matching has many good properties like Pareto optimality and stability. Moreover, in this case IMB selects the unique core allocation and truth-telling is a Nash equilibrium for students. If preferences satisfy a single peakedness condition, or have a single crossing property, then IMB is guaranteed to produce a non-wasteful matching. These properties guarantee also that the Deferred Acceptance algorithm (DA) and the Top Trading Cycles algorithm (TTC) produce the same matching as IMB. We compare these results with some well-known results about when DA is Pareto optimal, or when DA and TTC produce the same matching.