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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)


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.

Suggested Citation

  • LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," CORE Discussion Papers 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2010069

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    References listed on IDEAS

    1. 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.
    2. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    3. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
    4. 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.
    5. 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.
    6. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
    7. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    8. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 283-307, June.
    9. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
    10. Juan Moreno-Ternero, 2006. "Composition, Securement, and Concede-and-divide," Spanish Economic Review, Springer;Spanish Economic Association, vol. 8(3), pages 227-237, September.
    11. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
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    More about this item


    claims problems; lower bounds; concede-and-divide; minimal overlap rule;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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