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Integer solutions to bankruptcy problems with non-integer claims

Author

Listed:
  • Vito Fragnelli

    ()

  • Stefano Gagliardo

    ()

  • Fabio Gastaldi

    ()

Abstract

In this paper, we consider a bankruptcy problem with the additional constraint that the estate has to be assigned in integer unities; differently from the approaches by other authors, we allow for non-integer claims. This situation poses new questions on the existence and the uniqueness of the solution. We propose a new solution method that leads to the “box solution”, for which uniqueness may be guaranteed introducing a ranking on the claimants. Some examples complete the paper. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:3:p:892-933
    DOI: 10.1007/s11750-013-0304-x
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    References listed on IDEAS

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    1. Rodica Branzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2011. "A bonus-malus approach to project management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 495-512, December.
    2. Carmen Herrero & Ricardo Martínez, 2011. "Allocation problems with indivisibilities when preferences are single-peaked," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 453-467, December.
    3. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    4. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    5. Rodica Branzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2008. "A Flow Approach to Bankruptcy Problems," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(2), pages 146-153, September.
    6. Carmen Herrero Blanco & Ricardo Martínez, 2004. "Egalitarian Rules In Claims Problems With Indivisible Goods," Working Papers. Serie AD 2004-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    7. Carmen Herrero & Ricardo Martínez, 2008. "Balanced allocation methods for claims problems with indivisibilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 603-617, May.
    8. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    9. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
    10. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    11. 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. repec:ebl:ecbull:eb-17-00032 is not listed on IDEAS
    2. 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.
    3. Reiner Wolff, 2017. "The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm," Games, MDPI, Open Access Journal, vol. 8(1), pages 1-12, February.
    4. Vito Fragnelli & Gianfranco Gambarelli, 2014. "Further open problems in cooperative games," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 51-62.
    5. Vito Fragnelli & Stefano Gagliardo & Fabio Gastaldi, 2016. "Bankruptcy problems with non-integer claims: definition and characterizations of the ICEA Solution," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 88-130, April.
    6. repec:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0426-z is not listed on IDEAS

    More about this item

    Keywords

    Bankruptcy problems; Integer solutions; 91A12; 91B32;

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