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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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    2. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    3. Alcalde, José & Peris, Josep E., 2022. "Mixing solutions for claims problems," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 78-87.
    4. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2017. "Duality in land rental problems," MPRA Paper 80509, University Library of Munich, Germany.
    5. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "Compensation and sacrifice in the probabilistic rationing of indivisible units," European Journal of Operational Research, Elsevier, vol. 302(2), pages 740-751.
    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.
    7. Yang Zheng & Xuefeng Sang & Zhiwu Liu & Siqi Zhang & Pan Liu, 2022. "Water Allocation Management Under Scarcity: a Bankruptcy Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(9), pages 2891-2912, July.
    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. Chatterjee, Siddhartha & Ertemel, Sinan & Kumar, Rajnish, 2021. "Parametric Rules for State Contingent Claims," QBS Working Paper Series 2021/03, Queen's University Belfast, Queen's Business School.
    13. 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.
    14. 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.
    15. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Constrained multi-issue rationing problems," UB School of Economics Working Papers 2016/347, University of Barcelona School of Economics.

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