TTC Domains

TL;DR

This paper characterizes the Top Trading Cycles (TTC) mechanism's uniqueness in object reallocation problems under strict preferences, introducing the top-two condition as a key domain property.

Contribution

It introduces the top-two condition, a minimal richness property, and extends the characterization of TTC's uniqueness to all domains satisfying this condition.

Findings

TTC is uniquely characterized under the top-two condition.

Almost all domains failing the top-two condition admit non-TTC mechanisms.

The results unify prior findings and highlight the robustness of the TTC characterization.

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 introduce a richness property on preference domains -- the top-two condition -- and show that this characterization extends to all domains satisfying it. The condition requires that within any subset of objects, if two objects can each be most-preferred, they can also be ranked as the top two (in either order). We further show that almost all domains failing the top-two condition for a triple or quadruple of objects admit non-TTC mechanisms satisfying the axioms. These results unify prior findings on specific domains, demonstrate the robustness of Ekici (2024) characterization, and suggest a minimal richness requirement that may underlie it.