Pair rationality and top trading cycles on single-peaked and single-dipped domains

2026-09-30

AI Summary

This paper investigates the axiomatic characterization of the Top Trading Cycles (TTC) mechanism under single-peaked and single-dipped preference domains. Employing matching theory and axiomatic methods, we systematically analyze the applicability boundaries of Ekici and Yenmez’s characterization of TTC within restricted preference domains. Our findings reveal that this characterization fails in the single-peaked domain, whereas it holds in the single-dipped domain without requiring strategy-proofness. Furthermore, we demonstrate that the weakened conditions are not viable substitutes. This study clarifies the fundamental differences in the axiomatic foundations of TTC across distinct preference structures and refines the applicable scope of related theories, thereby providing a more precise theoretical basis for matching mechanism design under restricted preference domains.

Abstract

In a recent study, Ekici and Yenmez (2026) characterize top trading cycles (TTC) on the unrestricted domain by strategy-proofness, individual rationality, and pair rationality, uncovering a correspondence between the axiomatic foundations of TTC and deferred acceptance, matching theory's two canonical rules. We show that their characterization fails on the single-peaked domain, but it holds on the single-dipped domain even without strategy-proofness. They also show that pair rationality can be replaced in their characterization by two weaker conditions concerning agents' first and second choices. In contrast, this replacement fails on the single-dipped domain, even when strategy-proofness is imposed.

Problem

• top trading cycles
• pair rationality
• single-peaked domain
• single-dipped domain
• strategy-proofness

Innovation

• Top Trading Cycles
• Pair Rationality
• Single-peaked Domain
• Single-dipped Domain
• Strategy-proofness