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Coalitional Manipulation on Networks

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  • Biung-Ghi Ju

    (Department of Economics, The University of Kansas)

Abstract

We consider an abstract model of division problems where each agent is identi- fied by a characteristic vector. Agents are situated on a network (a non-directed graph) and any connected coalition can reallocate members¡¯ characteristics (e.g. reallocation of claims in bankruptcy problems). A reallocation-proof rule prevents any coalition from benefiting, in terms of its total award, through a reallocation. We offer a full characterization of reallocation-proof rules without any assumption on the network structure. This result yields a variety of useful corollaries for specific networks such as the complete network, trees, networks without a ¡°bridge¡± etc. Our model has various special examples such as bankruptcy, surplus sharing, cost sharing, income redistribution, social choice with transferable utility, etc.

Suggested Citation

  • 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.
    • Handle: RePEc:kan:wpaper:200410
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
    2. Calleja, Pedro & Llerena, Francesc, 2022. "Non-manipulability by clones in bankruptcy problems," Economics Letters, Elsevier, vol. 221(C).
    3. Pedro Calleja & Francesc Llerena, 2023. "Proportional clearing mechanisms in financial systems: an axiomatic approach," UB School of Economics Working Papers 2023/442, University of Barcelona School of Economics.
    4. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "Reassignment-proof rules for land rental problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 173-193, March.
    5. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2023. "Remarks on solidarity in bankruptcy problems when agents merge or split," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 61-64.
    6. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2015. "Non-manipulable rules for land rental problems," MPRA Paper 67334, University Library of Munich, Germany.
    7. William Thomson, 2016. "Non-bossiness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 665-696, October.
    8. 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.
    9. László Á. Kóczy, 2022. "Core-stability over networks with widespread externalities," Annals of Operations Research, Springer, vol. 318(2), pages 1001-1027, November.
    10. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    11. Sudhölter, Peter & Calleja, Pedro & Llerena, Francesc, 2023. "A note on solidarity in bankruptcy problems when agents merge or split," Discussion Papers on Economics 1/2023, University of Southern Denmark, Department of Economics.
    12. Calleja, Pedro & Llerena, Francesc, 2024. "Proportional clearing mechanisms in financial systems: An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    13. Takayuki Oishi & Gerard van der Laan & René van den Brink, 2018. "The Tort Law and the Nucleolus for Generalized Joint Liability Problems," Discussion Papers 37, Meisei University, School of Economics.
    14. Juarez, Ruben & Nitta, Kohei & Vargas, Miguel, 2021. "Coalitional efficient profit-sharing," Economics Letters, Elsevier, vol. 204(C).
    15. Zou, Zhengxing & Tan, Zhibin, 2023. "Axiomatizations of convex compromise rules for redistribution of non-negative income," Economics Letters, Elsevier, vol. 229(C).
    16. Christian Basteck & Frank Huettner, 2023. "Coalitional Manipulations and Immunity of the Shapley Value," Papers 2310.20415, arXiv.org.

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    More about this item

    Keywords

    Division problem; Coalitional manipulation; Network; Graph; Reallocationproofness;
    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

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