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Stability and fairness in models with a multiple membership

Author

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  • LE BRETON, Michel

    (Université de Toulouse 1, GREMAQ and IDEI, Toulouse, France)

  • MORENO-TERNERO, Juan D.

    (Universidad de Malaga, Spain; Universidad Pablo de Olavide, Seville, Spain; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • SAVVATEEV, Alexei

    (New Economic School, Moscow, Russia)

  • WEBER, Shlomo

    (Southern Methodist University, Dallas, USA and New Economic School, Moscow, Russia)

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 in- divisible, 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 on metric environments with indivisible projects. To do so, we explore, among other things, the performance of several well-known solutions (such as the Shapley value, the nucleolus, or the Dutta-Ray value) in these environments.

Suggested Citation

  • LE BRETON, Michel & MORENO-TERNERO, Juan D. & SAVVATEEV, Alexei & WEBER, Shlomo, 2010. "Stability and fairness in models with a multiple membership," LIDAM Discussion Papers CORE 2010079, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2010079
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    1. 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.
    2. 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.
    3. Messan Agbaglah, 2017. "Overlapping coalitions, bargaining and networks," Theory and Decision, Springer, vol. 82(3), pages 435-459, March.
    4. Sokolov, Denis, 2022. "Shapley value for TU-games with multiple memberships and externalities," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 76-90.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

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    More about this item

    Keywords

    stability; fairness; membership; coalition formation;
    All these keywords.

    JEL classification:

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

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