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Operators for the adjudication of conflicting claims

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  • Thomson, William
  • Yeh, Chun-Hsien

Abstract

We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A "rule" associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study "operators" on the space, that is, mappings that associate to each rule another one. Duality, claims truncation, and attribution of minimal rights are the operators we consider. We first establish a number of results linking them. Then, we determine which properties of rules are preserved under each of these operators, and which are not.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 143 (2008)
Issue (Month): 1 (November)
Pages: 177-198

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Handle: RePEc:eee:jetheo:v:143:y:2008:i:1:p:177-198

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Conflicting claims Division rules Operators Minimal rights Maximal claims Duality;

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References

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  1. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
  2. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer, vol. 13(1), pages 51-59, January.
  3. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
  4. Youngsub Chun & William Thomson, 2004. "Convergence under Replication of Rules to Adjudicate Conflicting Claims," RCER Working Papers 512, University of Rochester - Center for Economic Research (RCER).
  5. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  6. 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.
  7. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520.
  8. Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Biung-Ghi Ju & Eiichi Miyagawa & Toyotaka Sakai, 2003. "Non-Manipulable Division Rules in Claim Problems and Generalizations," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200307, University of Kansas, Department of Economics, revised Aug 2005.
  10. 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).
  11. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
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Citations

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Cited by:
  1. Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Osterdal, 2012. "Rationing in the presence of baselines," Working Papers 12.04, Universidad Pablo de Olavide, Department of Economics.
  2. Diego Dominguez, 2013. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Social Choice and Welfare, Springer, vol. 40(3), pages 663-678, March.
  3. JU, Biung-Ghi & MORENO-TERNERO, Juan D., . "Progressive and merging-proof taxation," CORE Discussion Papers RP -2280, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Østerdal, 2011. "A Unifying Framework for the Problem of Adjudicating Conflicting Claims," Discussion Papers 11-03, University of Copenhagen. Department of Economics.
  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. JU, Biung-Ghi & MORENO-TERNERO, Juan D., 2006. "Progressivity, inequality reduction and merging-proofness in taxation," CORE Discussion Papers 2006075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Kristof Bosmans & Luc Lauwers, 2007. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," Center for Economic Studies - Discussion papers ces0705, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  8. Marieke Quant & Peter Borm, 2011. "Random conjugates of bankruptcy rules," Social Choice and Welfare, Springer, vol. 36(2), pages 249-266, February.
  9. LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," CORE Discussion Papers 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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