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Harsanyi power solutions for cooperative games on voting structures

Author

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  • Encarnaciön Algaba

    (Matematica Aplicada II and Instituto de Matematicas de la Universidad de Sevilla, Escuela Superior de Ingenieros, Sevilla, Spain)

  • Sylvain Béal

    (Université de Bourgogne Franche-Comté, CRESE)

  • Eric Rémila

    (Université de Saint-Etienne, Gate)

  • Phillippe Solal

    (Université de Saint-Etienne, Gate)

Abstract

This paper deals with Harsanyi power solutions for cooperative games in which partial cooperation is based on specific union stable systems given by the winning coalitions derived from a voting game. This framework allows for analyzing new and real situations in which there exists a feedback between the economic influence of each coalition of agents and its political power. We provide an axiomatic characterization of the Harsanyi power solutions on the subclass of union stable systems arisen from the winning coalitions from a voting game when the influence is determined by a power index. In particular, we establish comparable axiomatizations, in this context, when considering the Shapley-Shubik power index, the Banzhaf index and the Equal division power index which reduces to the Myerson value on union stable systems. Finally, a new characterization for the Harsanyi power solutions on the whole class of union stable systems is provided and, as a consequence, a characterization of the Myerson value is obtained when the equal power measure is considered.

Suggested Citation

  • Encarnaciön Algaba & Sylvain Béal & Eric Rémila & Phillippe Solal, 2018. "Harsanyi power solutions for cooperative games on voting structures," Working Papers 2018-05, CRESE.
    • Handle: RePEc:crb:wpaper:2018-05
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    References listed on IDEAS

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    1. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 817-849, November.
    2. Béal, Sylvain & Moyouwou, Issofa & Rémila, Eric & Solal, Philippe, 2020. "Cooperative games on intersection closed systems and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 15-22.
    3. Clinton Gubong Gassi, 2024. "A Characterization of the Myerson value for cooperative games on voting structures," Working Papers 2024-10, CRESE.
    4. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.

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