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Non-Manipulable Division Rules in Claim Problems and Generalizations

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Author Info

  • 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)

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    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.

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    File URL: http://www.ku.edu/~bgju/2003Papers/200307Ju-Miyagawa-Sakai.pdf
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    Bibliographic Info

    Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 200307.

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    Length: 30 pages
    Date of creation: Dec 2003
    Date of revision: Aug 2005
    Publication status: Forthcoming in Journal of Economic Theory
    Handle: RePEc:kan:wpaper:200307

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    Related research

    Keywords: Reallocation-proofness; proportional rule; no advantageous reallocation; manipulation via merging or splitting.;

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    References

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    1. Moulin Herve, 1984. "Egalitarianisme and utilitarianism in quasi-linear bargaining," CEPREMAP Working Papers (Couverture Orange) 8417, CEPREMAP.
    2. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    3. 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.
    4. 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.
    5. 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.
    6. Gustavo Bergantiños & Juan Vidal-Puga, 2003. "Additive rules in bankruptcy problems and other related problems," Game Theory and Information 0304001, EconWPA.
    7. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    8. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    9. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    10. Biung-Ghi Ju, 2004. "Coalitional Manipulation on Networks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200410, University of Kansas, Department of Economics, revised Aug 2004.
    11. Majumdar, Dipjyoti, 2004. "An axiomatic characterization of Bayes' Rule," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 261-273, May.
    12. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
    13. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
    14. 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.
    15. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
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    Cited by:
    1. Biung-Ghi Ju & Juan D. Moreno-Ternero, 2006. "Progressivity, Inequality Reduction, and Merging-Proofness in Taxation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200603, University of Kansas, Department of Economics, revised Feb 2006.
    2. Ju, Biung-Ghi, 2013. "Coalitional manipulation on networks," Journal of Economic Theory, Elsevier, vol. 148(2), pages 627-662.
    3. SPRUMONT, Yves & MOULIN, Hervé, 2005. "Fair Allocation of Production Externalities: Recent Results," Cahiers de recherche 2005-22, Universite de Montreal, Departement de sciences economiques.
    4. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
    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. Biung-Ghi Ju, 2004. "Coalitional Manipulation on Communication Network," Econometric Society 2004 Far Eastern Meetings 563, Econometric Society.

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