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Lower bounds rule!

  • LUTTENS, Roland Iwan

    ()

    (Ghent University, SHERPPA, B-9000 Ghent, Belgium; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

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    We propose two axioms that introduce lower bounds into resource monotonicity requirements for rules for the problem of adjudicating conflicting claims. Suppose the amount to divide increases. The first axiom requires that two claimants whose lower bound changes equally experience an equal change in awards. The second axiom requires that extra resources are divided only among those claimants who experience a strictly positive change in their lower bound. We show that, in the two-claimant case, Concede-and-Divide is the only rule that satisfies both axioms when the axioms are defined over a large set of lower bounds that include the minimal rights lower bound and the secured lower bound. We also show that, in the n-claimant case where at least one claimant claims the total amount, the Minimal Overlap rule is the only rule that satisfies both axioms when the axioms are defined over the secured lower bound.

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    File URL: http://www.uclouvain.be/cps/ucl/doc/core/documents/coredp2010_69web.pdf
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    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2010069.

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    Date of creation: 01 Nov 2010
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    Handle: RePEc:cor:louvco:2010069
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    1. 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.
    2. 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.
    3. William Thomson & Chun-Hsien Yeh, 2006. "Operators for the adjudication of conflicting claims," RCER Working Papers 531, University of Rochester - Center for Economic Research (RCER).
    4. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
    5. William Thomson, 2007. "Two families of rules for the adjudication of conflicting claims," RCER Working Papers 535, University of Rochester - Center for Economic Research (RCER).
    6. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    7. MORENO-TERNERO, Juan D., . "Composition, securement, and concede-and-divide," CORE Discussion Papers RP -1895, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer, vol. 28(2), pages 283-307, 06.
    9. repec:cup:cbooks:9780521681599 is not listed on IDEAS
    10. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
    11. 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).
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