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Updating Claims in Bankruptcy Problems

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We reexamine the consistency axiom in bankruptcy problems and propose arguments in favor of an alternative definition of a reduced problem. The classical definition updates the size of the estate while keeping agents' claims unaffected. Instead, we suggest updating agents' claims along with the estate. The resulting consistency axiom characterizes the well-known Random Arrival rule as the unique bilaterally consistent extension of the Contested Garment rule to many agents. We also establish that our definition of a reduced bankruptcy problem corresponds to the definition of a reduced TU game proposed in Hart & Mas-Colell (Econometrica, 1989).

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  • M. Josune Albizuri & Justin Leroux & José Manuel Zarzuelo, 2008. "Updating Claims in Bankruptcy Problems," Cahiers de recherche 08-08, HEC Montréal, Institut d'économie appliquée.
    • Handle: RePEc:iea:carech:0808
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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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    3. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    4. 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.
    5. Sudholter, Peter, 1998. "Axiomatizations of Game Theoretical Solutions for One-Output Cost Sharing Problems," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 142-171, July.
    6. 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.
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    Cited by:

    1. Yan-an Hwang & Tsung-fu Wang, 2009. "Population monotonicity, consistency and the random arrival rule," Economics Bulletin, AccessEcon, vol. 29(4), pages 2816-2821.
    2. 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.
    3. Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "A random arrival rule for NTU-bankruptcy problems," Economics Letters, Elsevier, vol. 218(C).
    4. Morgenstern, Ilan & Domínguez, Diego, 2019. "A characterization of the random arrival rule for bankruptcy problems," Economics Letters, Elsevier, vol. 174(C), pages 214-217.
    5. M. Albizuri & J. Echarri & J. Zarzuelo, 2015. "A non-cooperative mechanism for the Shapley value of airport problems," Annals of Operations Research, Springer, vol. 235(1), pages 1-11, December.

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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