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NTU-Bankruptcy Problems : Consistency and the Relative Adjustment Principle

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  • Dietzenbacher, Bas

    (Tilburg University, Center For Economic Research)

  • Borm, Peter

    (Tilburg University, Center For Economic Research)

  • Estevez Fernandez, M.A.

    (Tilburg University, Center For Economic Research)

Abstract

This paper axiomatically studies bankruptcy problems with nontransferable utility by focusing on generalizations of consistency and the contested garment principle. On the one hand, we discuss several consistency notions and introduce the class of parametric bankruptcy rules which contains the proportional rule, the constrained relative equal awards rule, and the constrained relative equal losses rule. On the other hand, we introduce the class of adjusted bankruptcy rules and characterize the relative adjustment principle by truncation invariance, minimal rights first, and a weak form of relative symmetry.
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  • Dietzenbacher, Bas & Borm, Peter & Estevez Fernandez, M.A., 2017. "NTU-Bankruptcy Problems : Consistency and the Relative Adjustment Principle," Discussion Paper 2017-044, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:f023d53e-b84f-4520-aa5e-9c9ebc8e7de5
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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. 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.
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    5. Guni Orshan & Federico Valenciano & José M. Zarzuelo, 2003. "The Bilateral Consistent Prekernel, the Core, and NTU Bankruptcy Problems," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 268-282, May.
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    7. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    8. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
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    13. William Thomson, 2013. "Game-Theoretic Analysis Of Bankruptcy And Taxation Problems: Recent Advances," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
    14. 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.
    15. 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.
    16. Marco Mariotti & Antonio Villar, 2005. "The Nash rationing problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 367-377, September.
    17. 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.
    18. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    19. Peters, Hans & Tijs, Stef & Zarzuelo, Jose, 1994. "A reduced game property for the Kalai-Smorodinsky and egalitarian bargaining solutions," Mathematical Social Sciences, Elsevier, vol. 27(1), pages 11-18, February.
    20. Dietzenbacher, Bas & Estevez Fernandez, M.A. & Borm, Peter & Hendrickx, Ruud, 2016. "Proportionality, Equality, and Duality in Bankruptcy Problems with Nontransferable Utility," Other publications TiSEM 959bd6d8-7c49-4479-9fd3-b, Tilburg University, School of Economics and Management.
    21. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 2021. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 301(1), pages 65-80, June.
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    Cited by:

    1. Eun Jeong Heo & Jinhyuk Lee, 2023. "Allocating $$\hbox {CO}_2$$ CO 2 emissions: a dynamic claims problem," Review of Economic Design, Springer;Society for Economic Design, vol. 27(1), pages 163-186, February.
    2. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    3. Dietzenbacher, Bas, 2017. "Bankruptcy Games with Nontransferable Utility," Other publications TiSEM 1cc9f5ff-f889-43ec-93af-c, Tilburg University, School of Economics and Management.
    4. Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "A random arrival rule for NTU-bankruptcy problems," Economics Letters, Elsevier, vol. 218(C).
    5. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    6. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    7. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    8. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 2021. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 301(1), pages 65-80, June.
    9. Bas Dietzenbacher, 2023. "Generalizing the constrained equal awards rule," Theory and Decision, Springer, vol. 95(1), pages 131-150, July.

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    More about this item

    Keywords

    NTU-bankruptcy problem; axiomatic analysis; consistency; parametric bankruptcy rules; adjusted bankruptcy rules; relatived adjustment principle;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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