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Remarks on the integer Talmud solution for integer bankruptcy problems

Author

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  • Vito Fragnelli

    (Università degli Studi del Piemonte Orientale)

  • Fabio Gastaldi

    (Università degli Studi del Piemonte Orientale)

Abstract

In Fragnelli et al. (TOP 22:892–933, 2014; TOP 24:88–130, 2016), we considered a bankruptcy problem with the additional constraint that the estate has to be assigned in integer unities, allowing for non-integer claims; we dealt with the extension to our setting of the constrained equal losses solution and of the constrained equal awards solution. Here, we analyze the possibilities of extending the Talmud solution to the integer situation, starting from the existing approaches for the non-integer case; some of these approaches are compatible with the non-integer claims, but in order to comply with as much as possible of the approaches it is necessary to switch to integer claims.

Suggested Citation

  • Vito Fragnelli & Fabio Gastaldi, 2017. "Remarks on the integer Talmud solution for integer bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 127-163, April.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0426-z
    DOI: 10.1007/s11750-016-0426-z
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    References listed on IDEAS

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    1. Vito Fragnelli & Stefano Gagliardo & Fabio Gastaldi, 2014. "Integer solutions to bankruptcy problems with non-integer claims," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 892-933, October.
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    6. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    7. Carmen Herrero & Ricardo Martínez, 2008. "Up methods in the allocation of indivisibilities when preferences are single-peaked," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 272-283, December.
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    Cited by:

    1. Anirban Ghatak, 2022. "Estate Division Problem: The Core and The Godly Interference," Working papers 497, Indian Institute of Management Kozhikode.
    2. Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2020. "Nontransferable utility bankruptcy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 154-177, April.
    3. Reiner Wolff, 2017. "The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm," Games, MDPI, vol. 8(1), pages 1-12, February.

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