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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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Suggested Citation

  • 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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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    4. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    5. 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.
    6. 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.
    7. Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2020. "Nontransferable utility bankruptcy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 154-177, April.
    8. 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.
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    10. Carmen Herrero, 1997. "Endogenous reference points and the adjusted proportional solution for bargaining problems with claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 113-119.
    11. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    12. 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.
    13. 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.
    14. 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.
    15. 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. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 0. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 0, pages 1-16.
    2. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    3. 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.
    4. Dietzenbacher, Bas & Peters, Hans, 2018. "Characterizing NTU-bankruptcy rules using bargaining axioms," Research Memorandum 006, Maastricht University, Graduate School of Business and Economics (GSBE).

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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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