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

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  • Diego Dominguez

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

Abstract

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.

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Bibliographic Info

Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0705.

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Length: 19 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:cie:wpaper:0705

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Keywords: Claims problems; Lower bounds; Recursive methods.;

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References

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  1. 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.
  2. Nir Dagan, 1996. "New Characterizations of Old Bankruptcy Rules," Economic theory and game theory 002, Nir Dagan.
  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. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer, vol. 18(2), pages 327-386.
  5. Juan de Dios Moreno Ternero & Antonio Villar Notario, 2003. "The Talmud Rule And The Securement Of Agents? Awards," Working Papers. Serie AD 2003-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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Cited by:
  1. Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Osterdal, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Working Papers 12.01, Universidad Pablo de Olavide, Department of Economics.
  2. José M. Jiménez Gómez & Josep Enric Peris Ferrando, 2012. "Fair bound based solidarity," Working Papers. Serie AD 2012-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. 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).
  4. LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," CORE Discussion Papers 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. William Thomson, 2013. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update," RCER Working Papers 578, University of Rochester - Center for Economic Research (RCER).
  6. José M. Jiménez Gómez & María del Carmen Marco, 2008. "A New Approach for Bounding Awards in Bankruptcy Problems," Working Papers. Serie AD 2008-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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