Operators for the adjudication of conflicting claims
We consider the problem of dividing 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, attribution of minimal rights, and convex combinations are the four operators we consider. We first establish a number of results linking these operators, such as idempotence, commutativity, and distributivity. Then, we determine which properties of rules are preserved under each of these operators, and which are not.
|Date of creation:||Jun 2006|
|Date of revision:|
|Contact details of provider:|| Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.|
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.:
- Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
- Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- 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.
- Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
- 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.
- O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
- 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).
- 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.
- 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).
- 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.
- 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.
- 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.
- Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 241-261, 03.
When requesting a correction, please mention this item's handle: RePEc:roc:rocher:531. 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: (Richard DiSalvo)
If references are entirely missing, you can add them using this form.