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How to Cope with Division Problems under Interval Uncertainty of Claims?

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  • Brânzei, R.

    (Tilburg University, School of Economics and Management)

  • Dimitrov, D.A.

    (Tilburg University, School of Economics and Management)

  • Pickl, S.
  • Tijs, S.H.

    (Tilburg University, School of Economics and Management)

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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Suggested Citation

  • Brânzei, R. & Dimitrov, D.A. & Pickl, S. & Tijs, S.H., 2002. "How to Cope with Division Problems under Interval Uncertainty of Claims?," Other publications TiSEM 80f71e66-45c0-41a4-9077-8, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:80f71e66-45c0-41a4-9077-884e72178999
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    References listed on IDEAS

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    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    3. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    4. 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.
    5. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    6. 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.
    7. 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.
    8. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    9. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    10. 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.
    11. Tijs, S. H. & Brânzei, R., 2017. "Cost sharing in a joint project," Center for Mathematical Economics Working Papers 336, Center for Mathematical Economics, Bielefeld University.
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    1. Brânzei, R. & Dall'Aglio, M. & Tijs, S.H., 2008. "Interval Game Theoretic Division Rules," Other publications TiSEM 6e6afacf-9cae-4f70-bf75-7, Tilburg University, School of Economics and Management.
    2. 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.
    3. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    4. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    5. 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.
    6. 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.
    7. 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.
    8. Rodica Branzei & Marco Dall’Aglio, 2009. "Allocation rules incorporating interval uncertainty," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(2), pages 19-28.
    9. 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.
    10. Alparslan-Gok, S.Z. & Miquel, S. & Tijs, S.H., 2008. "Cooperation under Interval Uncertainty," Other publications TiSEM 9a01bd57-964d-4e71-8508-7, Tilburg University, School of Economics and Management.
    11. 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.
    12. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Cores and Stable Sets for Interval-Valued Games," Other publications TiSEM cb5233c0-1616-48e8-983c-6, Tilburg University, School of Economics and Management.
    13. 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.
    14. Alparslan-Gok, S.Z. & Miquel, S. & Tijs, S.H., 2008. "Cooperation under Interval Uncertainty," Discussion Paper 2008-09, Tilburg University, Center for Economic Research.
    15. Long, Yan & Sethuraman, Jay & Xue, Jingyi, 2021. "Equal-quantile rules in resource allocation with uncertain needs," Journal of Economic Theory, Elsevier, vol. 197(C).
    16. Brânzei, R. & Dall'Aglio, M. & Tijs, S.H., 2008. "Interval Game Theoretic Division Rules," Discussion Paper 2008-97, Tilburg University, Center for Economic Research.
    17. M. Hinojosa & A. Mármol & F. Sánchez, 2013. "Extended proportionality in division problems with multiple references," Annals of Operations Research, Springer, vol. 206(1), pages 183-195, July.
    18. 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.
    19. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
    20. 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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