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How to cope with division problems under interval uncertainty of claims?

Author

Listed:
  • Branzei,R.
  • Dimitrov,D.

    (Institute of Mathematical Economics, Bielefeld University)

  • Pickl,S.
  • Tijs,S.

Abstract

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Branzei,R. & Dimitrov,D. & Pickl,S. & Tijs,S., 2002. "How to cope with division problems under interval uncertainty of claims?," Center for Mathematical Economics Working Papers 339, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:339
    as

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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-339.pdf
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    References listed on IDEAS

    as
    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    3. Rodica Brânzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2002. "Two Approaches to the Problem of Sharing Delay Costs in Joint Projects," Annals of Operations Research, Springer, vol. 109(1), pages 359-374, January.
    4. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    5. 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.
    6. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    7. Stef Tijs & Rodica Branzei, 2002. "Cost sharing in a joint project," Center for Mathematical Economics Working Papers 336, Center for Mathematical Economics, Bielefeld University.
    8. Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January.
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    Citations

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    Cited by:

    1. Yan-an Hwang & Ming-chuan Chen, 2012. "A new axiomatization of the Shapley value under interval uncertainty," Economics Bulletin, AccessEcon, vol. 32(1), pages 799-810.
    2. Brânzei, R. & Dall'Aglio, M. & Tijs, S.H., 2008. "Interval Game Theoretic Division Rules," Discussion Paper 2008-97, Tilburg University, Center for Economic Research.
    3. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    4. S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 99-109, March.
    5. 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.
    6. Rodica Branzei & Marco Dall'aglio, 2009. "Allocation rules incorporating interval uncertainty," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 19-28.
    7. Alparslan-Gok, S.Z. & Miquel, S. & Tijs, S.H., 2008. "Cooperation under Interval Uncertainty," Discussion Paper 2008-09, Tilburg University, Center for Economic Research.
    8. Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2010. "The truncated core for games with upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 645-656, October.
    9. repec:spr:compst:v:69:y:2009:i:1:p:99-109 is not listed on IDEAS
    10. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Cores and Stable Sets for Interval-Valued Games," Discussion Paper 2008-17, Tilburg University, Center for Economic Research.
    11. Yan-An Hwang & Wei-Yuan Yang, 2014. "A note on potential approach under interval games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 571-577, July.
    12. Hinojosa Ramos, Miguel Ángel & López Sánchez, Ana Dolores, 2011. "Regla de reparto proporcional con referencias múltiples: aplicación al caso de agregación y actualización de probabilidades || A Proportional Rule for the Division Problems with Multiple References: A," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 12(1), pages 65-80, December.
    13. Luisa Carente & Balbina Casas-Mendez & Ignacio Carcia-Jurado & Anne van den Nouweland, 2007. "The Truncated Core for Games with Limited Aspirations," Department of Economics - Working Papers Series 1010, The University of Melbourne.
    14. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
    15. Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2008. "Coalitional Interval Games for Strategic Games in Which Players Cooperate," Theory and Decision, Springer, vol. 65(3), pages 253-269, November.

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    Keywords

    claims; division problems;

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