Lower bounds and recursive methods for the problem of adjudicating conflicting claims
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.
|Date of creation:||Sep 2007|
|Date of revision:|
|Contact details of provider:|| Postal: Camino a Sta. Teresa 930, Mexico, D.F. 10700|
Phone: +525 628 4197
Fax: +525 628 4058
Web page: http://cie.itam.mx/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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).
- 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.
- Nir Dagan, 1996.
"New Characterizations of Old Bankruptcy Rules,"
Economic theory and game theory
002, Nir Dagan.
- Diego Dominguez & William Thomson, 2004.
"A New Solution to the Problem of Adjudicating Conflicting Claims,"
RCER Working Papers
511, University of Rochester - Center for Economic Research (RCER).
- 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.
When requesting a correction, please mention this item's handle: RePEc:cie:wpaper:0705. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Diego Dominguez)
If references are entirely missing, you can add them using this form.