This paper studies the possibility of strategy-proof rules yielding satisfactory solutions to matching problems …. Alcalde and Barberá (1994) show that effcient and individually rational matching rules are manipulable in the one …-to-one matching model. We pursue the possibility of strategy-proof matching rules by relaxing effciency to the weaker condition of …

-proof mechanism that is constrained efficient, i.e. that always produces a stable matching that is not Pareto-dominated by another … stable matching. We characterize all solvable priority structures satisfying the following two restrictions: (A) Either there … three types of solvable priority structures: The strict type, the house allocation with existing tenants (HET) type, where …