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

Nir Dagan and Oscar Volij

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Abstract

We analyze the problem of extending a given bilateral principle of justice to a consistent n-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.

International Journal of Game Theory 26:11-25 (1997)

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Cited by

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  2. Youngsub Chun, Equivalence of axioms for bankruptcy problems, International Journal of Game Theory 28:511-520 (1999)
  3. Marek M. Kaminski, 'Hydraulic' rationing, Mathematical Social Sciences 40:131-155 (2000)
  4. William Thomson, On the axiomatic method and its recent applications to game theory and resource allocation, Social Choice and Welfare 18:327-386 (2001)
  5. Somdeb Lahiri, Axiomatic characterizations of the CEA solution for rationing problems, European Journal of Operational Research 131:162-170 (2001)
  6. Toru Hokari and William Thomson, Claims problems and weighted generalizations of the Talmud rule, Economic Theory 21:241-261 (2003)
  7. William Thomson, Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey, Mathematical Social Sciences 45:249-297 (2003)
  8. Joe Malkevitch, Resolving bankruptcy claims, Feature Column, Monthly Essays on Mathematical Topics, AMS website (March 2005)
  9. Roberto Serrano and Ken-Ichi Shimomura, A comparison of the average prekernel and the prekernel, Mathematical Social Sciences 52:288-301 (2006)
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  12. Diego Dominguez and William Thomson, A new solution to the problem of adjudicating conflicting claims, Economic Theory 28:283-307 (2006)
  13. William Thomson, On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach, Review of Economic Design 11:225-251 (2007)
  14. William Thomson, The two-agent claims-truncated proportional rule has no consistent extension: a constructive proof, Economics Letters 98:59-65 (2008)
  15. Toru Hokari and William Thomson, On properties of division rules lifted by bilateral consistency, Journal of Mathematical Economics 44:1057-1071 (2008)