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Envy-free reallocations when preferences are single-dipped

Author

Listed:
  • Hanssen, Pauline

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

  • Dietzenbacher, Bas

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

Abstract

This paper studies reallocation problems where preferences are single-dipped and each agent is endowed with a share of one unit of an infinitely divisible and non-disposable commodity. We focus on several envy-freeness requirements: standard envy-freeness, restricted envy-freeness, net trade envy-freeness, and proportional envy-freeness. It turns out that none of these envy freeness requirements is compatible with Pareto optimality for each reallocation problem. However, for standard envy-freeness, net trade envy-freeness, and proportional envy-freeness, at most one allocation is Pareto optimal. For restricted envy-freeness, at most one allocation is Pareto optimal and individually rational. For each of the four envy-freeness requirements, we characterize this unique allocation for each reallocation problem where it exists.

Suggested Citation

  • Hanssen, Pauline & Dietzenbacher, Bas, 2026. "Envy-free reallocations when preferences are single-dipped," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2026007
    DOI: 10.26481/umagsb.2026007
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    References listed on IDEAS

    as
    1. Bettina Klaus & Hans Peters & Ton Storcken, 1997. "Reallocation of an infinitely divisible good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 305-333.
    2. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    3. Zhen Zhao & Shinji Ohseto, 2022. "Strategy-proof and fair reallocation with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(4), pages 791-800, May.
    4. Yamamura, Hirofumi, 2023. "Uniform rules for the allocation problem with single-dipped preferences when free-disposal is possible," Economics Letters, Elsevier, vol. 230(C).
    5. Osei, Ernest Lartey & Majumdar, Dipjyoti, 2025. "Strategyproof and fair allocation of a perfectly divisible private commodity with (restricted) single-dipped preferences," Economics Letters, Elsevier, vol. 255(C).
    6. Tamura, Yuki, 2023. "Object reallocation problems with single-dipped preferences," Games and Economic Behavior, Elsevier, vol. 140(C), pages 181-196.
    7. Bettina Klaus, 2001. "original papers : Uniform allocation and reallocation revisited," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 85-98.
    8. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
    9. Dietzenbacher, Bas & Tamura, Yuki, 2024. "Fair and efficient allocations when preferences are single-dipped," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    10. Doudou Gong & Bas Dietzenbacher & Hans Peters, 2024. "Mechanisms and axiomatics for division problems with single-dipped preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(3), pages 789-813, November.
    11. Dietzenbacher, Bas & Tamura, Yuki, 2023. "Stable and efficient reallocations when preferences are single-dipped," Economics Letters, Elsevier, vol. 231(C).
    12. Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    13. Kazuhiko Hashimoto & Takuma Wakayama, 2021. "Fair reallocation in economies with single-peaked preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 773-785, September.
    14. Klaus, Bettina, 2001. "Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object," Games and Economic Behavior, Elsevier, vol. 34(1), pages 64-82, January.
    15. Doghmi Ahmed, 2013. "Nash Implementation in Private Good Economies when Preferences are Single-Dipped with Best Indifferent Allocations," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 35-42, October.
    16. Lars Ehlers, 2002. "Probabilistic allocation rules and single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 325-348.
    17. Fumiya Inoue & Hirofumi Yamamura, 2023. "Binary mechanism for the allocation problem with single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 647-669, May.
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    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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