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On the Convergence of the Generalized Ibn Ezra Value


  • Louis Mesnard

    () (Univ. Bourgogne Franche-Comté)


Ibn Ezra (Sefar ha-Mispar (The Book of the Number, in Hebrew), Verona (German trans: Silberberg M. (1895)). Kauffmann, Frankfurt am Main, 1146), Rabinovitch (Probability and statistical inference in medieval Jewish literature. University of Toronto Press, Toronto, 1973) and O’Neill (Math Soc Sci 2(4):345–371, 1982) proposed a method for solving the “rights arbitration problem” (one of the historical problems of “bankruptcy”) for n claimants when the estate E is equal to the largest claim. However, when the greatest claim is for less than the estate, the question of what to do with the difference between E and the largest claim is posed. Alcalde et al.’s (Econ Theory 26(1):103–114, 2005) Generalized Ibn Ezra Value (GiEV), solves the problem in T iterations, of n steps. By using Monte-Carlo experiments, we show that: (i) T grows linearly with the number of claimants, which makes GiEV rapidly impracticable for real applications. (ii) The more E is close to the total claim d, the more T grows: T linearly grows when E exponentially approaches d by a factor 10. Moreover, we proved through theory that GiEV fails to provide a solution in a finite number of iterations for the trivial case E = d, whereas it should obviously find a solution in one iteration. So, even if GiEV is convergent, the sum of claims d appears as an asymptote: the number of iterations tends to infinite when the estate E approaches the claims total d. We conclude that GiEV is inefficient and usable only when: (1) the number of claimants is low, and (2) the estate E is largely lower than the total claims d.

Suggested Citation

  • 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.
  • Handle: RePEc:kap:compec:v:54:y:2019:i:3:d:10.1007_s10614-018-9863-0
    DOI: 10.1007/s10614-018-9863-0

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    References listed on IDEAS

    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. Chun, Youngsub & Thomson, William, 2005. "Convergence under replication of rules to adjudicate conflicting claims," Games and Economic Behavior, Elsevier, vol. 50(2), pages 129-142, February.
    3. 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.
    4. José Alcalde & María Marco & José Silva, 2005. "Bankruptcy games and the Ibn Ezra’s proposal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 103-114, July.
    5. 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.
    6. Gustavo Bergantiños & Luciano Méndez-Naya, 2001. "Additivity in bankruptcy problems and in allocation problems," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(3), pages 223-229.
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    More about this item


    Game theory; Ibn Ezra; Bankruptcy; Rights arbitration; Cooperative game; Convergence; Monte-Carlo experiments;

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • 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
    • B1 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925
    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology


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