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Bankruptcy Games And The Ibn Ezra'S Proposal

Author

Listed:
  • 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.

Suggested Citation

  • José Alcalde & José Angel Silva & María del Carmen Marco, 2002. "Bankruptcy Games And The Ibn Ezra'S Proposal," Working Papers. Serie AD 2002-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2002-28
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    References listed on IDEAS

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    2. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 283-295, February.
    3. Louis Mesnard, 2019. "On the Convergence of the Generalized Ibn Ezra Value," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1065-1084, October.
    4. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 109-128, June.
    5. José-manuel Giménez-gómez & Cori Vilella, 2017. "Recursive methods for discrete claims problems," Economics Bulletin, AccessEcon, vol. 37(3), pages 1653-1665.
    6. 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.
    7. José-Manuel Giménez-Gómez & Josep E. Peris & María-José Solís-Baltodano, 2017. "Resource Allocation with Warranties in Claims Problems," QM&ET Working Papers 17-4, University of Alicante, D. Quantitative Methods and Economic Theory.
    8. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    9. Miguel Ángel Mirás Calvo & Iago Núñez Lugilde & Carmen Quinteiro Sandomingo & Estela Sánchez Rodríguez, 2023. "Refining the Lorenz‐ranking of rules for claims problems on restricted domains," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 526-558, September.
    10. José-Manuel Giménez-Gómez & M. Marco-Gil, 2014. "A new approach for bounding awards in bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 447-469, August.
    11. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 547-569, August.

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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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