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Annals of Operations Research

, Volume 254, Issue 1–2, pp 449–465 | Cite as

The reverse TAL-family of rules for bankruptcy problems

  • René van den Brink
  • Juan D. Moreno-TerneroEmail author
Original Paper

Abstract

This paper analyzes a family of rules for bankruptcy problems that generalizes the so-called reverse Talmud rule and encompasses both the constrained equal-awards rule and the constrained equal-losses rule. The family, introduced by van den Brink et al. (Eur J Oper Res 228:413–417, 2013), is a counterpart to the so-called TAL-family of rules, introduced and studied by Moreno-Ternero and Villar (Soc Choice Welf 27:231–249, 2006a), and it is included within the so-called CIC-family of rules introduced by Thomson (Soc Choice Welf 31:667–692, 2008). We provide a systematic study of the structural properties of the rules within the family, as well as its connections with the existing related literature.

Keywords

Bankruptcy problems Reverse TAL-family Reverse Talmud rule Equal awards Equal losses 

JEL Classification

D63 

References

  1. Arin, J., Benito-Ostolaza, J., & Inarra, E. (2015). The RTAL-family of rules for bankruptcy problems: A characterization. Mimeo: University of the Basque Country.Google Scholar
  2. Aumann, R. J., & Maschler, M. (1985). Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory, 36, 195–213.CrossRefGoogle Scholar
  3. Bergantiños, G., & Lorenzo, L. (2008). The equal award principle in problems with constraints and claims. European Journal of Operational Research, 1881, 224–239.CrossRefGoogle Scholar
  4. van den Brink, R., Funaki, Y., & van der Laan, G. (2013). Characterization of the reverse Talmud bankruptcy rule by exemption and exclusion properties. European Journal of Operational Research, 228, 413–417.CrossRefGoogle Scholar
  5. Casas-Méndez, B., Fragnelli, V., & García-Jurado, I. (2011). Weighted bankruptcy rules and the museum pass problem. European Journal of Operational Research, 215, 161–168.CrossRefGoogle Scholar
  6. Chambers, C. P. (2005). Asymmetric rules for claims problems without homogeneity. Games and Economic Behavior, 54, 241–260.CrossRefGoogle Scholar
  7. Chambers, C. P., & Moreno-Ternero, J. D. (2017). Taxation and poverty. Social Choice and Welfare, 48, 153–175.CrossRefGoogle Scholar
  8. Chambers, C. P., & Thomson, W. (2002). Group order preservation and the proportional rule for bankruptcy problems. Mathematical Social Sciences, 44, 235–252.CrossRefGoogle Scholar
  9. Chun, Y. (1999). Equivalence of axioms for bankruptcy problems. International Journal of Game Theory, 28, 511–520.CrossRefGoogle Scholar
  10. Chun, Y., Schummer, J., & Thomson, W. (2001). Constrained egalitarianism: A new solution for claims problems. Seoul Journal of Economics, 14, 269–297.Google Scholar
  11. Curiel, I., Maschler, M., & Tijs, S. (1987). Bankruptcy games. Zeitschrift für Operations Research, 31, A143–A159.Google Scholar
  12. Flores-Szwagrzak, K. (2015). Priority classes and weighted constrained equal-awards rules for the claims problem. Journal of Economic Theory, 160, 36–45.CrossRefGoogle Scholar
  13. Giménez-Gómez, J. M., & Osorio, A. (2015). Why and how to differentiate in claims problems? An axiomatic approach. European Journal of Operational Research, 241, 842–850.CrossRefGoogle Scholar
  14. Giménez-Gómez, J. M., & Peris, J. E. (2014). A proportional approach to claims problems with a guaranteed minimum. European Journal of Operational Research, 232, 109–116.CrossRefGoogle Scholar
  15. Harless, P. (2017). Endowment additivity and the weighted proportional rules for adjudicating conflicting claims. Economic Theory, 63, 755–781.CrossRefGoogle Scholar
  16. Herrero, C., & Villar, A. (2002). Sustainability in bankruptcy problems. TOP, 10, 261–273.CrossRefGoogle Scholar
  17. Hougaard, J. L., Moreno-Ternero, J. D., & Østerdal, L. P. (2012). A unifying framework for the problem of adjudicating conflicting claims. Journal of Mathematical Economics, 48, 107–114.CrossRefGoogle Scholar
  18. Hougaard, J. L., Moreno-Ternero, J. D., & Østerdal, L. P. (2013a). Rationing in the presence of baselines. Social Choice and Welfare, 40, 1047–1066.CrossRefGoogle Scholar
  19. Hougaard, J. L., Moreno-Ternero, J. D., & Østerdal, L. P. (2013b). Rationing with baselines: The composition extension operator. Annals of Operations Research, 211, 179–191.CrossRefGoogle Scholar
  20. Huijink, S., Borm, P. E. M., Kleppe, J., & Reijnierse, J. H. (2015). Bankruptcy and the per capita nucleolus: The claim-and-right rules family. Mathematical Social Sciences, 77, 15–31.CrossRefGoogle Scholar
  21. Ju, B.-G., & Moreno-Ternero, J. D. (2017). Fair allocation of disputed properties. International Economic Review, 58(4).Google Scholar
  22. Moreno-Ternero, J. D. (2007). Bankruptcy rules and coalitional manipulation. International Game Theory Review, 9, 105–118.CrossRefGoogle Scholar
  23. Moreno-Ternero, J. D. (2011a). Voting over piece-wise linear tax rules. Journal of Mathematical Economics, 47, 29–36.CrossRefGoogle Scholar
  24. Moreno-Ternero, J. D. (2011b). A coalitional procedure leading to a family of bankruptcy rules. Operations Research Letters, 39, 1–3.CrossRefGoogle Scholar
  25. Moreno-Ternero, J. D., & Roemer, J. (2006). Impartiality, solidarity, and priority in the theory of justice. Econometrica, 74, 1419–1427.CrossRefGoogle Scholar
  26. Moreno-Ternero, J. D., & Roemer, J. (2012). A common ground for resource and welfare egalitarianism. Games and Economic Behavior, 75, 832–841.CrossRefGoogle Scholar
  27. Moreno-Ternero, J. D., & Villar, A. (2004). The Talmud rule and the securement of agents’ awards. Mathematical Social Sciences, 47, 245–257.CrossRefGoogle Scholar
  28. Moreno-Ternero, J. D., & Villar, A. (2006a). The TAL-family of rules for bankruptcy problems. Social Choice and Welfare, 27, 231–249.CrossRefGoogle Scholar
  29. Moreno-Ternero, J. D., & Villar, A. (2006b). On the relative equitability of a family of taxation rules. Journal of Public Economic Theory, 8, 283–291.CrossRefGoogle Scholar
  30. Moulin, H. (1987). Equal or proportional division of a surplus, and other methods. International Journal of Game Theory, 16, 161–186.CrossRefGoogle Scholar
  31. Moulin, H. (2000). Priority rules and other asymmetric rationing methods. Econometrica, 68, 643–684.CrossRefGoogle Scholar
  32. O’Neill, B. (1982). A problem of rights arbitration from the Talmud. Mathematical Social Sciences, 2, 345–371.CrossRefGoogle Scholar
  33. Pulido, M., Sanchez-Soriano, J., & Llorca, N. (2002). Game theory techniques for university management: An extended bankruptcy model. Annals of Operations Research, 109, 129–142.CrossRefGoogle Scholar
  34. Pulido, M., Borm, P., Hendricx, R., Llorca, N., & Sanchez-Soriano, J. (2008). Compromise solutions for bankruptcy situations with references. Annals of Operations Research, 158, 133–141.CrossRefGoogle Scholar
  35. Thomson, W. (2003). Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: A survey. Mathematical Social Sciences, 45, 249–297.CrossRefGoogle Scholar
  36. Thomson, W. (2008). Two families of rules for the adjudication of conflicting claims. Social Choice and Welfare, 31, 667–692.CrossRefGoogle Scholar
  37. Thomson, W. (2013). The theory of fair allocation. Princeton: Princeton University Press (forthcoming).Google Scholar
  38. Thomson, W. (2015a). Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update. Mathematical Social Sciences, 74, 41–59.CrossRefGoogle Scholar
  39. Thomson, W. (2015b). For claims problems, a compromise between the constrained equal awards and proportional rules. Economic Theory, 60, 452–495.CrossRefGoogle Scholar
  40. Thomson, W. (2017). How to divide when there isn’t enough: From the Talmud to game theory. Econometric Society Monograph. Cambridge, MA: Cambridge University Press.Google Scholar
  41. Timoner, P., & Izquierdo, J. M. (2016). Rationing problems with ex-ante conditions. Mathematical Social Sciences, 79, 46–52.CrossRefGoogle Scholar
  42. Yeh, C.-H. (2006). Protective properties and the constrained equal-awards rule for claims problems: A note. Social Choice and Welfare, 27, 221–230.CrossRefGoogle Scholar
  43. Young, H. P. (1987). On dividing an amount according to individual claims or liabilities. Mathematics of Operations Research, 12, 398–414.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • René van den Brink
    • 1
  • Juan D. Moreno-Ternero
    • 2
    • 3
    Email author
  1. 1.Department of Econometrics and Operations Research, Tinbergen InstituteVU UniversityAmsterdamThe Netherlands
  2. 2.Department of EconomicsUniversidad Pablo de OlavideSevilleSpain
  3. 3.COREUniversité catholique de LouvainLouvain-la-NeuveBelgium

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