An Ancient Bankruptcy Solution Makes Economic Sense

  • Anh H. Ly
  • Michael Zakharevich
  • Olga Kosheleva
  • Vladik Kreinovich
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 760)


While econometrics is a reasonable recent discipline, quantitative solutions to economic problem have been proposed since the ancient times. In particular, solutions have been proposed for the bankruptcy problem: how to divide the assets between the claimants? One of the challenges of analyzing ancient solutions to economics problems is that these solutions are often presented not as a general algorithm, but as a sequence of examples. When there are only a few such example, it is often difficult to convincingly extract a general algorithm from them. This was the case, for example, for the supposedly fairness-motivated Talmudic solution to the bankruptcy problem: only in the mid 1980s, the Nobelist Robert Aumann succeeded in coming up with a convincing general algorithm explaining the original examples. What remained not so clear in Aumann’s explanation is why namely this algorithm best reflects the corresponding idea of fairness. In this paper, we find a simple economic explanation for this algorithm.



This work was supported in part by the National Science Foundation grant HRD-1242122 (Cyber-ShARE Center of Excellence).


  1. 1.
    Aumann, R.J., Machler, M.: Game theoretic analysis of a banruptcy problem from the telmud. J. Econ. Theor. 36, 195–213 (1985)CrossRefGoogle Scholar
  2. 2.
    Epstein, L. (ed.): The Babylonian Talmud. Soncino, London (1935)Google Scholar
  3. 3.
    Hurwicz, L.: Optimality Criteria for Decision Making Under Ignorance, Cowles Commission Discussion Paper, Statistics, No. 370 (1951)Google Scholar
  4. 4.
    Kaminsky, M.: ‘Hydraulic’ Rationing. Math. Soc. Sci. 40, 131–155 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kreinovich, V.: Decision making under interval uncertainty (and beyond). In: Guo, P., Pedrycz, W. (eds.) Human-Centric Decision-Making Models for Social Sciences. Springer Verlag, pp. 163–193 (2014)Google Scholar
  6. 6.
    Luce, R.D., Raiffa, R.: Games and Decisions: Introduction and Critical Survey. Dover, New York (1989)zbMATHGoogle Scholar
  7. 7.
    Nash, J.: Two-person cooperative games. Econometrica 21, 128–140 (1953)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Shechter, S.: How the talmud divides an estate among creditors. In: Bridging Mathematics, Statistics, Engineering, and Technology: Controbutions from the Seminar on Mathematical Sciences and Applications. Springer Verlag, Berlin, Heidelberg, New York (2012)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Anh H. Ly
    • 1
  • Michael Zakharevich
    • 2
  • Olga Kosheleva
    • 3
  • Vladik Kreinovich
    • 3
  1. 1.Banking University of Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.SeeCure Systems, Inc.BelmontUSA
  3. 3.University of Texas at El PasoEl PasoUSA

Personalised recommendations