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Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties

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  • van den Brink, René
  • Funaki, Yukihiko
  • van der Laan, Gerard

Abstract

The Reverse Talmud rule for bankruptcy problems applies the Constrained Equal Awards rule (CEA rule) for ‘large’ amounts of the estate, while it applies the Constrained Equal Losses rule (CEL rule) for ‘small’ amounts of the estate. The CEA rule, respectively CEL rule, can be axiomatized using the Exemption and Exclusion properties respectively. There is no rule that satisfies both these two properties. In this paper we axiomatize the Reverse Talmud rule by using compatible weaker versions of the Exemption and Exclusion properties.

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  • van den Brink, René & Funaki, Yukihiko & van der Laan, Gerard, 2013. "Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties," European Journal of Operational Research, Elsevier, vol. 228(2), pages 413-417.
  • Handle: RePEc:eee:ejores:v:228:y:2013:i:2:p:413-417
    DOI: 10.1016/j.ejor.2013.01.052
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    4. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2017. "Duality in land rental problems," MPRA Paper 80509, University Library of Munich, Germany.
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    6. René Brink & Juan D. Moreno-Ternero, 2017. "The reverse TAL-family of rules for bankruptcy problems," Annals of Operations Research, Springer, vol. 254(1), pages 449-465, July.
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    8. Zhengxing Zou & René Brink & Yukihiko Funaki, 2022. "Sharing the surplus and proportional values," Theory and Decision, Springer, vol. 93(1), pages 185-217, July.
    9. Arin, J. & Benito-Ostolaza, J. & Inarra, E., 2017. "The reverse Talmud family of rules for bankruptcy Problems: A characterization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 43-49.
    10. Juan D. Moreno-Ternero, 2017. "A Talmudic Approach to Bankruptcy Problems," Working Papers 17.01, Universidad Pablo de Olavide, Department of Economics.
    11. 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.
    12. Juan D. Moreno‐Ternero & Min‐Hung Tsay & Chun‐Hsien Yeh, 2022. "Strategic justifications of the TAL family of rules for bankruptcy problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 92-102, March.
    13. José, Alcalde & Peris, Josep E., 2020. "Mixing Solutions in Claims Problems," QM&ET Working Papers 20-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    14. 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 School of Economics.

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