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Operators for the adjudication of conflicting claims

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Author Info
William Thomson () (University of Rochester)
Chun-Hsien Yeh (Institute of Economics, Academia Sinica, Taipei 115, Taiwan.)

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Abstract

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.

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_531.pdf
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Publisher Info
Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 531.

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Length: 37 pages
Date of creation: Jun 2006
Date of revision:
Handle: RePEc:roc:rocher:531

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Postal: UNIVERSITY OF ROCHESTER, CENTER FOR ECONOMIC RESEARCH, DEPARTMENT OF ECONOMICS, HARKNESS 231 ROCHESTER NEW YORK 14627 U.S.A.

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Related research
Keywords: Conflicting claims Division rules Operators Minimal rights Maximal claims Duality Convexity.

Other versions of this item:

Find related papers by 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

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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.:
  1. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520. [Downloadable!] (restricted)
  2. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03. [Downloadable!] (restricted)
  3. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  4. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. Herrero, C., 1998. "Minimal Rights in Claims Problems," Papers 98-20, Valencia - Instituto de Investigaciones Economicas.
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  7. 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. [Downloadable!] (restricted)
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  8. 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. [Downloadable!]
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  9. 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. [Downloadable!] (restricted)
  10. Nir Dagan, 1996. "New Characterizations of Old Bankruptcy Rules," Economic theory and game theory 002, Nir Dagan. [Downloadable!]
    Other versions:
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