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Domains where the uniform rule is well behaved

Author

Listed:
  • Souvik Roy

    (Indian Statistical Institute)

  • Soumyarup Sadhukhan

    (Indian Institute of Technology Kanpur)

Abstract

We consider the problem of dividing one unit of an infinitely divisible object among a finite number of agents. We provide a characterization of all single-peaked domains on which the uniform rule is the unique division rule satisfying efficiency, strategy-proofness, and equal treatment of equals (ETE). Next, we consider non-single-peaked domains and provide a characterization of all such domains on which the uniform rule satisfies efficiency, strategy-proofness, and ETE. We also show that under some mild richness conditions the uniform rule is the unique rule satisfying the mentioned properties on these domains. Finally, we provide a wide range of applications to justify the usefulness of our results.

Suggested Citation

  • Souvik Roy & Soumyarup Sadhukhan, 2024. "Domains where the uniform rule is well behaved," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 1033-1071, September.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:3:d:10.1007_s00182-024-00906-2
    DOI: 10.1007/s00182-024-00906-2
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    References listed on IDEAS

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    1. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 229-246, March.
    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. Hideyuki Mizobuchi & Shigehiro Serizawa, 2006. "Maximal Domain for Strategy-proof Rules in Allotment Economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 195-210, August.
    4. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
    5. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "Strategy-proof Rules on Partially Single-peaked Domains," MPRA Paper 82267, University Library of Munich, Germany.
    6. Stiglitz, J. E., 1974. "The demand for education in public and private school systems," Journal of Public Economics, Elsevier, vol. 3(4), pages 349-385, November.
    7. John A. Weymark, 1999. "Sprumont's characterization of the uniform rule when all single-peaked preferences are admissible," Review of Economic Design, Springer;Society for Economic Design, vol. 4(4), pages 389-393.
    8. Hans Peters & Gert-Jan Otten & Oscar Volij, 1996. "Two characterizations of the uniform rule for division problems with single-peaked preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 291-306.
    9. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    10. Ching, Stephen & Serizawa, Shigehiro, 1998. "A Maximal Domain for the Existence of Strategy-Proof Rules," Journal of Economic Theory, Elsevier, vol. 78(1), pages 157-166, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Division problems; Efficiency; Strategy-proofness; Equal treatment of equals; Single-peaked preferences; Non-single-peaked preferences; The uniform rule;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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