TTC Domains

Abstract: We study the object reallocation problem under strict preferences. On the unrestricted domain, Ekici (2024) showed that the Top Trading Cycles (TTC) mechanism is the unique mechanism that is individually rational, pair efficient, and strategyproof. We provide an alternative proof of this result, assuming only minimal richness of the unrestricted domain. This allows us to identify a broad class of restricted domains, those satisfying our top-two condition, on which the characterization continues to hold. The condition requires that, within any subset of objects, if two objects can each be most-preferred, they can also be the top two most-preferred objects (in both possible orders). We show that this condition is also necessary in the special case of three objects. These results unify and strengthen prior findings on specific domains such as single-peaked and single-dipped domain, and more broadly, offer a useful criterion for analyzing restricted preference domains.