International Journal of Game Theory

, Volume 26, Issue 1, pp 11–25 | Cite as

Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems

  • Nir Dagan
  • Oscar Volij


We analyze the problem of extending a given bilateral principle of justice to a consistentn-creditor bankruptcy rule. Based on the bilateral principle, we build a family of binary relations on the set of creditors in order to make bilateral comparisons between them. We find that the possibility of extending a specific bilateral principle of justice in a consistent way is closely related to the quasi-transitivity of the binary relations mentioned above.


Economic Theory Game Theory Binary Relation Division Rule Fair Division 
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  1. Aumann RJ, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the talmud. Journal of Economic Theory 36: 195–213Google Scholar
  2. Dagan N, Volij O (1993) The bankruptcy problem, a cooperative bargaining approach. Mathematical Social Sciences 26: 287–297Google Scholar
  3. Dagan N, Serrano R, Volij O (1994) A non-cooperative view of consistent bankruptcy rules. Discussion Paper 9411, CentER for Economic Research Tilburg, The NetherlandsGoogle Scholar
  4. Fishburn PC (1970) Utility theory for decision making, John Wiley and Sons, NYGoogle Scholar
  5. Lensberg T (1987) Stability and collective rationality. Econometrica 55: 935–961Google Scholar
  6. Maschler M Owen G (1989) The consistent shapley value for hyperplane games. International Journal of Game Theory 18: 389–407Google Scholar
  7. Peleg B (1986) On the reduced game property and its converse. International Journal of Game Theory 15:187–200Google Scholar
  8. Sen A (1969) Quasi-transitivity, rational choice and collective decisions. Review of Economic Studies 36: 381–393Google Scholar
  9. Thomson W (1990) The consistency principle. In: Ichiishi T, Neyman A, Tauman Y (Eds) Game Theory and Applications. Academic Press San Diego CAGoogle Scholar
  10. Thomson W (1994) Consistent extensions. Mathematical Social Sciences 28: 35–49Google Scholar
  11. Young HP (1987) On dividing an amount according to individual claims or liabilities. Math Opr Res 12: 398–414Google Scholar
  12. Young HP (1988) Distributive justice in taxation. Journal of Economic Theory 44: 321–335Google Scholar

Copyright information

© Physica-Verlag 1997

Authors and Affiliations

  • Nir Dagan
    • 1
  • Oscar Volij
    • 2
  1. 1.Department of EconomicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of EconomicsBrown UniversityProvidenceUSA

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