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Partial-implementation invariance and claims problems

Author

Listed:
  • Dietzenbacher, Bas

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

  • Tamura, Yuki
  • Thomson, William

Abstract

In the context of claims problems, we formulate an invariance axiom of a rule with respect to its “partial implementation”: having applied the rule to a problem and distributed their awards to some of the claimants, we consider the problem obtained by setting the claims of these claimants equal to zero and decreasing the endowment by the sum of their awards; we require that in this problem the rule assigns to each remaining claimant the same amount as it did initially. We formulate several variants of this requirement of “partial-implementation invariance” and a “converse” of it. We investigate how it relates to known axioms and ask whether it is preserved under certain “operators” that have been defined on the space of rules. Our main result is a fixed-population characterization of a family of rules introduced and characterized by Young (1987) in a variable-population framework, known as the “parametric rules”.

Suggested Citation

  • Dietzenbacher, Bas & Tamura, Yuki & Thomson, William, 2023. "Partial-implementation invariance and claims problems," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2023002
    DOI: 10.26481/umagsb.2023002
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    References listed on IDEAS

    as
    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    3. Dagan, Nir & Volij, Oscar, 1993. "The bankruptcy problem: a cooperative bargaining approach," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 287-297, November.
    4. Biung†Ghi Ju & Juan D. Moreno†Ternero, 2017. "Fair Allocation Of Disputed Properties," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(4), pages 1279-1301, November.
    5. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    6. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    7. Biung-Ghi Ju, 2003. "Manipulation via merging and splitting in claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 205-215, October.
    8. 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.
    9. Oscar Volij & Nir Dagan, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 11-25.
    10. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    11. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    12. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    13. 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.
    14. 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.
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    More about this item

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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