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Lower bounds and recursive methods for the problem of adjudicating conflicting claims


  • Diego Dominguez

    () (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))


For the problem of adjudicating conflicting claims, we study lower bounds on the awards of each agent. We propose extending a lower bound by performing the following operation: (i) for each problem, assign the lower bound and revise the problem accordingly; (ii) assign the bound of the revised problem. The “recursive-extension” of a bound is the lower bound obtained by recursive application of this operation. We provide necessary and sufficient conditions on a lower bound for there to be a unique rule satisfying its recursive-extension. We show that, under these conditions, the rule satisfying the recursive-extension of a bound is the unique rule satisfying the following property: the awards assigned by a rule should be obtainable in two ways: (i) directly applying the rule to the problem or (ii) first assigning the bound and revising the problem accordingly, and then applying the rule to the revised problem. Then, we study whether this procedure leads to well-behaved lower bounds.

Suggested Citation

  • Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
  • Handle: RePEc:cie:wpaper:0705

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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. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    3. 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.
    4. 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.
    5. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
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    Cited by:

    1. Giménez-Gómez, José Manuel & Peris, Josep E., 2012. "Fair bounds based solidarity," Working Papers 2072/203162, Universitat Rovira i Virgili, Department of Economics.
    2. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
    3. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    4. Giménez Gómez, José M. (José Manuel) & Peris, Josep E. & Solís Baltodano, María José, 2017. "Resource allocation with warranties in claims problems," Working Papers 2072/292437, Universitat Rovira i Virgili, Department of Economics.
    5. Yeh, Chun-Hsien, 2008. "Secured lower bound, composition up, and minimal rights first for bankruptcy problems," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 925-932, September.
    6. José M. Jiménez Gómez, 2010. "Why people reach intermediate agreements? Axiomatic and strategic justifications," Working Papers. Serie AD 2010-29, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    7. José-Manuel Giménez-Gómez & Josep Peris, 2014. "Mediation in claims problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 5(4), pages 357-375, November.
    8. José-Manuel Giménez-Gómez & M. Marco-Gil, 2014. "A new approach for bounding awards in bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 447-469, August.
    9. repec:ebl:ecbull:eb-17-00032 is not listed on IDEAS
    10. Giménez-Gómez, José-Manuel & Peris, Josep E. & Solís-Baltodano, María-José, 2017. "Resource Allocation with Warranties in Claims Problems," QM&ET Working Papers 17-4, University of Alicante, D. Quantitative Methods and Economic Theory.
    11. LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," CORE Discussion Papers 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item


    Claims problems; Lower bounds; Recursive methods.;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • 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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