Robust minimal instability of the top trading cycles mechanism
Article [Version of Record]
Publisher(s)Université de Montréal. Département de sciences économiques.
In the context of priority-based resource allocation, we formulate methods to compare assignments in terms of their stability as binary relations (on the set of possible assignments) that depend on the preference and the priority proﬁle. We introduce three basic properties, stability preferred, separability, and consistency, that a reasonable stability comparison should satisfy. We show that, for any stability comparison satisfying the three properties, the top trading cycles (TTC) mechanism is minimally unstable among eﬃcient and strategy-proof mechanisms in one-to-one matching. An important consequence is the robustness of a recent result by Abdulkadiroĝlu et al. (2019), which uses a particular stability comparison method where an assignment is more stable than another assignment if the set of blocking pairs in the former assignment is a subset of the set of blocking pairs in the latter assignment. Our unifying approach covers basically all natural comparison methods and it includes many cardinal stability comparison methods as special cases.