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Stability and fairness in models with a multiple membership

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  • Michel Le Breton
  • Juan Moreno-Ternero
  • Alexei Savvateev
  • Shlomo Weber

Abstract

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus. Copyright Springer-Verlag 2013

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  • Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:3:p:673-694
    DOI: 10.1007/s00182-011-0304-8
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    Cited by:

    1. Stefan Ambec & Yann Kervinio, 2016. "Cooperative decision-making for the provision of a locally undesirable facility," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 119-155, January.
    2. Heinrich H. Nax, 2014. "A Note on the Core of TU-cooperative Games with Multiple Membership Externalities," Games, MDPI, vol. 5(4), pages 1-13, October.
    3. Messan Agbaglah, 2017. "Overlapping coalitions, bargaining and networks," Theory and Decision, Springer, vol. 82(3), pages 435-459, March.
    4. Wolfgang Buchholz & Alexander Haupt & Wolfgang Peters, 2016. "Equity as a Prerequisite for Stability of Cooperation on Global Public Good Provision," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 61-78, September.
    5. M. J. Albizuri & J. M. Echarri & J. M. Zarzuelo, 2018. "A Non-cooperative Mechanism Yielding the Nucleolus of Airport Problems," Group Decision and Negotiation, Springer, vol. 27(1), pages 153-163, February.
    6. Sokolov, Denis, 2022. "Shapley value for TU-games with multiple memberships and externalities," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 76-90.
    7. M. Albizuri & J. Echarri & J. Zarzuelo, 2015. "A non-cooperative mechanism for the Shapley value of airport problems," Annals of Operations Research, Springer, vol. 235(1), pages 1-11, December.
    8. Musatov, D. & Savvateev, A., 2022. "Mathematical models of stable jurisdiction partitions: A survey of results and new directions," Journal of the New Economic Association, New Economic Association, vol. 54(2), pages 12-38.
    9. Andrey Zaytsev & Ekaterina Mihel & Nikolay Dmitriev & Dmitry Alferyev & Ungvari Laszlo, 2024. "Optimization of Interaction with Counterparties: Selection Game Algorithm under Uncertainty," Mathematics, MDPI, vol. 12(13), pages 1-27, July.

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    More about this item

    Keywords

    Stability; Fairness; Membership; Coalition formation; C71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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