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A consistent talmudic rule for division problems with multiple references

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Listed:
  • M. Hinojosa

    ()

  • A. Mármol

    ()

  • F. Sánchez

Abstract

We consider an extension of the classic division problem with claims, division problems with multiple references. We show that the theory of cooperative games is able to provide a single-valued allocation rule for this class of problems. Moreover, this rule can be related with the Talmud rule for the classic division problem, as in Aumann and Maschler (J. Econ. Theory 36, 195–213, 1985 ). Finally, we establish the consistency and other basic properties of the rule. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • M. Hinojosa & A. Mármol & F. Sánchez, 2012. "A consistent talmudic rule for division problems with multiple references," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 661-678, October.
  • Handle: RePEc:spr:topjnl:v:20:y:2012:i:3:p:661-678
    DOI: 10.1007/s11750-010-0158-4
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    References listed on IDEAS

    as
    1. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    2. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2007. "A composite run-to-the-bank rule for multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 339-352, April.
    3. Serrano, Roberto, 1995. "Strategic bargaining, surplus sharing problems and the nucleolus," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 319-329.
    4. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    5. M. Pulido & P. Borm & R. Hendrickx & N. Llorca & J. Sánchez-Soriano, 2008. "Compromise solutions for bankruptcy situations with references," Annals of Operations Research, Springer, vol. 158(1), pages 133-141, February.
    6. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    7. Lorenzo-Freire, Silvia & Alonso-Meijide, Jose M. & Casas-Mendez, Balbina & Hendrickx, Ruud, 2007. "Balanced contributions for TU games with awards and applications," European Journal of Operational Research, Elsevier, vol. 182(2), pages 958-964, October.
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    Cited by:

    1. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    2. repec:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9673-9 is not listed on IDEAS
    3. Miguel Hinojosa & Amparo Mármol, 2014. "Multi-commodity rationing problems with maxmin payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 353-370, June.
    4. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Constrained multi-issue rationing problems," UB Economics Working Papers 2016/347, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.

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