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Bankruptcy Games And The Ibn Ezra'S Proposal

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Author Info

  • José Alcalde

    ()
    (Universidad de Alicante)

  • José Angel Silva

    (Universidad de Alicante)

  • María del Carmen Marco

    (Universidad Politécnica de Cartagena)

Abstract

This paper follows the interpretation of the bankruptcy problems in terms of TU games given in O'Neill (1982). In this context we propose the analysis of the Transition Game associated to each bankruptcy problem. We explore an old solution described by Ibn Ezra in the XII century. Firstly, we study the extension of the Ibn Ezra's proposal by O'Neill (1982), the Minimal Overlap solution. We provide a characterization of this value and show that it can be understood as the composition of the Ibn Ezra solution and the Constrained Equal Loss rule. Secondly, we introduce a new way of extending the Ibn Ezra's proposal, the Generalized Ibn Ezra solution, by imposing that the general distribution principle in which is inspired remains fixed. The characterization of our proposal clarifies the analogies and differences between the two ways of generalizing the Ibn Ezra's proposal.

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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2002-28.

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Length: 48 pages
Date of creation: Dec 2002
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2002-28

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Keywords: Bankruptcy Problems; Cooperative Games; Ibn Ezra's proposal; Minimal Overlap solution.;

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References

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  1. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  2. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  3. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  4. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  5. Moulin, Herve, 1994. "Serial Cost-Sharing of Excludable Public Goods," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 305-25, April.
  6. 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.
  7. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  8. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  9. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154241, Tilburg University.
  10. 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.
  11. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
  12. 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.
  13. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  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.
  15. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer, vol. 13(1), pages 51-59, January.
  16. Gustavo Bergantiños & Luciano Méndez-Naya, 2001. "Additivity in bankruptcy problems and in allocation problems," Spanish Economic Review, Springer, vol. 3(3), pages 223-229.
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Citations

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Cited by:
  1. José M. Jiménez Gómez & María del Carmen Marco, 2008. "A New Approach for Bounding Awards in Bankruptcy Problems," Working Papers. Serie AD 2008-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, vol. 46(2), pages 283-295, February.
  3. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer, vol. 50(3), pages 547-569, August.
  4. William Thomson, 2007. "Two families of rules for the adjudication of conflicting claims," RCER Working Papers 535, University of Rochester - Center for Economic Research (RCER).
  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).
  6. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer, vol. 31(1), pages 109-128, June.

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