# Priority and proportionality in bankruptcy

- 54 Downloads

## Abstract

We study the problem of distributing the liquidation value of a bankrupt firm among its creditors (O’Neill, Math Soc Sci 2(4):345–371, 1982; Aumann and Maschler, J Econ Theory 36(2):195–213, 1985). Real-life distribution rules prioritize predetermined creditor groups, dividing the amount assigned to each group proportionally to claims. We provide the first axiomatic characterization of such rules. In addition to the classical consistency and continuity axioms, these rules are characterized by the following properties: (1) bankruptcy problems with the same claims and where each claimant’s award is positive in each problem can be solved either jointly or separately without altering the recommended awards, (2) a dual property specifying that bankruptcy problems with the same claims and where each claimant’s loss is positive can be solved either jointly or separately without altering the recommended awards.

## JEL classification

D70 D63 D71## Notes

## References

- Alcalde J, del Carmen Marco-Gil M, Silva-Reus JA (2014) The minimal overlap rule: restrictions on mergers for creditors’ consensus. Top 22(1):363–383CrossRefGoogle Scholar
- Arin J, Benito-Ostolaza J, Inarra E (2017) The reverse talmud family of rules for banktruptcy problems: a characterization. Math Soc Sci 89:43–49CrossRefGoogle Scholar
- Aumann R, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36(2):195–213CrossRefGoogle Scholar
- Bergantiños G, Méndez-Naya L (2001) Additivity in bankruptcy problems and in allocation problems. Span Econ Rev 3(3):223–229CrossRefGoogle Scholar
- Bergantiños G, Vidal-Puga JJ (2004) Additive rules in bankruptcy problems and other related problems. Math Soc Sci 47(1):87–101CrossRefGoogle Scholar
- Chun Y (1988) The proportional solution for rights problems. Math Soc Sci 15(3):231–246CrossRefGoogle Scholar
- Chun Y (1999) Equivalence of axioms for bankruptcy problems. Int J Game Theory 28(4):511–520CrossRefGoogle Scholar
- Csoka P, Herings J (2016) An axiomatization of the proportional rule in financial networks. Maastricht University Working paperGoogle Scholar
- de Frutos M (1999) Coalitional manipulation in a bankruptcy problem. Rev Econ Design 4(3):255–272CrossRefGoogle Scholar
- Flores-Szwagrzak K (2015) Priority classes and weighted constrained equal awards rules for the claims problem. J Econ Theory 160:36–55CrossRefGoogle Scholar
- Harless P (2017) Endowment additivity and the weighted proportional rules for adjudicating conflicting claims. Econ Theory 63(3):755–781CrossRefGoogle Scholar
- Hokari T, Thomson W (2003) Claims problems and weighted generalizations of the Talmud rule. Econ Theory 21(2):241–261CrossRefGoogle Scholar
- Ju B, Miyagawa E, Sakai T (2007) Non-manipulable division rules in claim problems and generalizations. J Econ Theory 132:1–26CrossRefGoogle Scholar
- Marchant T (2008) Scale invariance and similar invariance conditions for bankruptcy problems. Soc Choice Welfare 31(4):693–707CrossRefGoogle Scholar
- Moreno-Ternero J (2006) Proportionality and non-manipulability in bankruptcy problems. Int Game Theory Rev 8(01):127–139CrossRefGoogle Scholar
- Moulin H (1987) Equal or proportional division of a surplus, and other methods. Int J Game Theory 16(3):161–186CrossRefGoogle Scholar
- Moulin H (2000) Priority rules and other asymmetric rationing methods. Econometrica 68(3):643–684CrossRefGoogle Scholar
- Moulin H (2002) Axiomatic cost and surplus-sharing. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier, Amsterdam, pp 289–357CrossRefGoogle Scholar
- O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2(4):345–371CrossRefGoogle Scholar
- Roth AE (1988) The Shapley value: essays in honor of Lloyd S. Shapley. Cambridge University Press, New YorkCrossRefGoogle Scholar
- Shapley L (1953) A value for \(n\)-person games. Ann Mat Stud 28:307–317Google Scholar
- Stovall J (2014a) Asymmetric parametric division rules. Games Econ Behav 84(1):87–110CrossRefGoogle Scholar
- Stovall J (2014b) Collective rationality and monotone path division rules. J Econ Theory 154:1–24CrossRefGoogle Scholar
- Thomson W (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45(3):249–297CrossRefGoogle Scholar
- Thomson W (2011) Consistency and its converse: an introduction. Rev Econ Design 15(4):257–291CrossRefGoogle Scholar
- Thomson W (2015) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update. Math Soc Sci 74:41–59CrossRefGoogle Scholar
- Thomson W (2016) A new characterization of the proportional rule for claims problems. Econ Lett 154:255–257CrossRefGoogle Scholar
- Thomson W (2019) How to divide when there isn’t enough: from Aristotle, the Talmud, and Maimonides to the Axiomatics of Resource Allocation. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Young P (1987) On dividing an amount according to claims or liabilities. Math Oper Res 12(3):397–414CrossRefGoogle Scholar
- Young P (1988) Distributive justice in taxation. J Econ Theory 44(2):321–335CrossRefGoogle Scholar
- Young P (1994) Equity: in theory and practice. Princeton University Press, PrincetonGoogle Scholar