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Non-Manipulable Division Rules in Claim Problems and Generalizations

Author

Listed:
  • Biung-Ghi Ju

    (Department of Economics, The University of Kansas)

  • Eiichi Miyagawa

    (Department of Economics, Columbia University)

  • Toyotaka Sakai

    (Department of Economics, University of Rochester)

Abstract

This paper studies the problem of allocating divisible resources among agents based on their characteristics. A simple example is the bankruptcy problem, which allocates the liquidation value of a bankrupted firm to creditors based on their claims. By allowing agents' characteristics to be multi-dimensional and varying the meaning of variables in the model, our model subsumes a number of existing and new alloca- tion problems, such as the problems of cost sharing, social choice under transferable utilities, income redistribution, bankruptcy with multiple assets, probability updat- ing, and probability aggregation. We characterize allocation rules under which no group of agents can increase the total amount they receive by transferring their characteristics within the group. A number of existing and new results in specific problems are obtained as corollaries.

Suggested Citation

  • 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.
  • Handle: RePEc:kan:wpaper:200307
    as

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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. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    3. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 49-67, January.
    4. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    5. Ju, Biung-Ghi, 2013. "Coalitional manipulation on networks," Journal of Economic Theory, Elsevier, vol. 148(2), pages 627-662.
    6. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    7. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2004. "Additive rules in bankruptcy problems and other related problems," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 87-101, January.
    8. Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January.
    9. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    10. Majumdar, Dipjyoti, 2004. "An axiomatic characterization of Bayes' Rule," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 261-273, May.
    11. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    12. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    13. Chambers, Christopher P. & Thomson, William, 2002. "Group order preservation and the proportional rule for the adjudication of conflicting claims," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 235-252, December.
    14. 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.
    15. 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.
    16. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer;Society for Economic Design, vol. 4(3), pages 255-272.
    17. 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.
    18. 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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    More about this item

    Keywords

    Reallocation-proofness; proportional rule; no advantageous reallocation; manipulation via merging or splitting.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D30 - Microeconomics - - Distribution - - - General
    • 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
    • H26 - Public Economics - - Taxation, Subsidies, and Revenue - - - Tax Evasion and Avoidance

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