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Bankruptcy Games And The Ibn Ezra'S Proposal

  • José Alcalde


    (Universidad de Alicante)

  • José Angel Silva

    (Universidad de Alicante)

  • María del Carmen Marco

    (Universidad Politécnica de Cartagena)

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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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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  1. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Other publications TiSEM 1855e4e3-7392-4ef0-a073-8, Tilburg University, School of Economics and Management.
  2. 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.
  3. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  4. 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.
  5. Nir Dagan, 1996. "New Characterizations of Old Bankruptcy Rules," Economic theory and game theory 002, Nir Dagan.
  6. 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.
  7. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  8. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  9. Gustavo Bergantiños & Luciano Méndez-Naya, 2001. "Additivity in bankruptcy problems and in allocation problems," Spanish Economic Review, Springer, vol. 3(3), pages 223-229.
  10. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
  11. 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.
  12. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  13. Moulin, Herve, 1994. "Serial Cost-Sharing of Excludable Public Goods," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 305-25, April.
  14. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  15. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  16. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
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