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Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency

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  • Pinaki Mandal

Abstract

In the object reallocation problem, achieving Pareto-efficiency is desirable, but may be too demanding for implementation purposes. In contrast, pair-efficiency, which is the minimal efficiency requirement, is more suitable. Despite being a significant relaxation, however, pair-efficiency ensures Pareto-efficiency for any strategy-proof and individually rational rule when agents' preferences are unrestricted. What if agents' preferences have specific restricted structures, such as single-peakedness or single-dippedness? We often encounter such situations in real-world scenarios. This study aims to investigate whether pair-efficiency is sufficient to ensure Pareto-efficiency in such cases. Our main contribution in this paper is establishing the equivalence between pair-efficiency and Pareto-efficiency when dealing with single-peaked or single-dipped preference profiles. This equivalence holds without needing to assume any other properties of the rule. We further show that both the single-peaked domain and the single-dipped domain are the "maximal" domains where this equivalence holds.

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  • Pinaki Mandal, 2025. "Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency," Papers 2506.15169, arXiv.org.
    • Handle: RePEc:arx:papers:2506.15169
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    References listed on IDEAS

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    1. Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.
    2. Allan M. Feldman, 1973. "Bilateral Trading Processes, Pairwise Optimally, and Pareto Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(4), pages 463-473.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. Hu, Xinquan & Zhang, Jun, 2024. "Characterization of Top Trading Cycles with single-dipped preferences," Economics Letters, Elsevier, vol. 241(C).
    5. Ekici, Özgün, 2024. "Pair-efficient reallocation of indivisible objects," Theoretical Economics, Econometric Society, vol. 19(2), May.
    6. 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.
    7. Ekici, Özgün & Sethuraman, Jay, 2024. "Characterizing the TTC rule via pair-efficiency: A short proof," Economics Letters, Elsevier, vol. 234(C).
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