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

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Author Info

  • 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.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-339.pdf
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 339.

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Date of creation: 2002
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Handle: RePEc:bie:wpaper:339

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Related research

Keywords: claims; division problems;

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References

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  1. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  2. 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.
  3. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  5. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
  6. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer, vol. 13(1), pages 51-59, January.
  7. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  8. Brânzei, R. & Ferrari, G. & Fragnelli, V. & Tijs, S.H., 2002. "Two approaches to the problem of sharing delay costs in joint projects," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91324, Tilburg University.
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Citations

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Cited by:
  1. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2003. "Shapley-like values for interval bankruptcy games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121815, Tilburg University.
  2. 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.
  3. 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.
  4. 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.
  5. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
  6. 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 Reference," 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.
  7. 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.
  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, vol. 39(4), pages 645-656, October.
  9. S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Computational Statistics, Springer, vol. 69(1), pages 99-109, March.
  10. Brânzei, R. & Dall'Aglio, M. & Tijs, S.H., 2008. "Interval Game Theoretic Division Rules," Discussion Paper 2008-97, Tilburg University, Center for Economic Research.
  11. William Thomson, 2013. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update," RCER Working Papers 578, University of Rochester - Center for Economic Research (RCER).

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