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A New Solution to the Problem of Adjudicating Conflicting Claims

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  • Diego Dominguez

    ()
    (University of Rochester)

  • William Thomson

    ()
    (University of Rochester)

Abstract

For the problem of adjudicating conflicting claims, we consider the requirement that each agent should receive at least 1/n his claim truncated at the amount to divide, where n is the number of claimants (Moreno-Ternero and Villar, 2004a). We identify two families of rules satisfying this bound. We then formulate the requirement that for each problem, the awards vector should be obtainable in two equivalent ways, (i) directly or (ii) in two steps, first assigning to each claimant his lower bound and then applying the rule to the appropriately revised problem. We show that there is only one rule satisfying this requirement. We name it the "recursive rule", as it is obtained by a recursion. We then undertake a systematic investigation of the properties of the rule.

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_511.pdf
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Bibliographic Info

Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 511.

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Length: 34 pages
Date of creation: Nov 2004
Date of revision:
Handle: RePEc:roc:rocher:511

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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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Keywords: claims problems; recursive rule.;

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  1. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
  2. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer, vol. 13(1), pages 51-59, January.
  3. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
  4. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  5. Dagan, N. & Volij, O., 1994. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Discussion Paper 1994-23, Tilburg University, Center for Economic Research.
  6. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  7. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  8. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Chun, Youngsub & Thomson, William, 2005. "Convergence under replication of rules to adjudicate conflicting claims," Games and Economic Behavior, Elsevier, vol. 50(2), pages 129-142, February.
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