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

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  • Ozgun Ekici
  • M. Bumin Yenmez

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.

Suggested Citation

  • Ozgun Ekici & M. Bumin Yenmez, 2026. "Pair rationality and top trading cycles on single-peaked and single-dipped domains," Papers 2609.39163, arXiv.org.
    • Handle: RePEc:arx:papers:2609.39163
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    References listed on IDEAS

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    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    2. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 417-435, May.
    3. Hu, Xinquan & Zhang, Jun, 2024. "Characterization of Top Trading Cycles with single-dipped preferences," Economics Letters, Elsevier, vol. 241(C).
    4. Tamura, Yuki, 2023. "Object reallocation problems with single-dipped preferences," Games and Economic Behavior, Elsevier, vol. 140(C), pages 181-196.
    5. Ekici, Özgün, 2024. "Pair-efficient reallocation of indivisible objects," Theoretical Economics, Econometric Society, vol. 19(2), May.
    6. Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.
    7. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
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