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A New Approach for Bounding Awards in Bankruptcy Problems

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  • Giménez-Gómez, José Manuel
  • Marco Gil, M. Carmen

Abstract

The solution for the ‘Contested Garment Problem’, proposed in the Babylonic Talmud, suggests that each agent should receive at least some part of the resources whenever the demand overcomes the available amount. In this context, we propose a new method to define lower bounds on awards, an idea that has underlied the theoretical analysis of bankruptcy problems from its beginning (O’Neill, 1982) to present day (Dominguez and Thomson, 2006). Specifically, starting from the fact that a society establishes its own set of ‘Commonly Accepted Equity Principles’, our proposal ensures to each agent the smallest amount she gets according to all the admissible rules. As in general this new bound will not exhaust the estate, we analyze its recursive application for different sets of equity principles. Keywords: Bankruptcy problems, Bankruptcy rules, Lower bounds, Recursive process

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Paper provided by Universitat Rovira i Virgili, Department of Economics in its series Working Papers with number 2072/182719.

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Date of creation: 2012
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Handle: RePEc:urv:wpaper:2072/182719

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Keywords: Fallida; 33 - Economia;

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  1. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
  2. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
  3. Diego Dominguez & William Thomson, 2004. "A New Solution to the Problem of Adjudicating Conflicting Claims," RCER Working Papers 511, University of Rochester - Center for Economic Research (RCER).
  4. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  5. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  6. Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.
  7. Volij, Oscar & Dagan, Nir & Serrano, Roberto, 1997. "A Non-Cooperative View of Consistent Bankruptcy Rules," Staff General Research Papers 5130, Iowa State University, Department of Economics.
  8. José Alcalde & María Marco & José Silva, 2005. "Bankruptcy games and the Ibn Ezra’s proposal," Economic Theory, Springer, vol. 26(1), pages 103-114, 07.
  9. Carmen Herrero & Antonio Villar, 2002. "Sustainability in bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 10(2), pages 261-273, December.
  10. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer, vol. 40(4), pages 791-807, November.
  11. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
  12. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  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. 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.
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Cited by:
  1. Giménez-Gómez, José Manuel, 2011. "A way to play bankruptcy problems," Working Papers 2072/169781, Universitat Rovira i Virgili, Department of Economics.
  2. Alcalde, José & Marco_Gil, María del Carmen & Silva, José A., 2012. "The Minimal Overlap Rule: Restrictions on Mergers for Creditors' Consensus," QM&ET Working Papers 12-1, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica.
  3. Peris, Josep E. & Jiménez-Gómez, José M., 2012. "Solidarity and uniform rules in bankruptcy problems," QM&ET Working Papers 12-8, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica.
  4. José M. Jiménez Gómez & Josep Enric Peris Ferrando, 2012. "Fair bound based solidarity," Working Papers. Serie AD 2012-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. William Thomson, 2013. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update," RCER Working Papers 578, University of Rochester - Center for Economic Research (RCER).

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