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The Shapley-Shubik power index for dichotomous multi-type games

Author

Listed:
  • Sébastien Courtin

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Zéphirin Nganmeni

    (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

  • Bertrand Tchantcho

    (ENSPY - Ecole Nationale Supérieure Polytechnique de Yaoundé - UY1 - Université de Yaoundé I)

Abstract

This work focuses on multi-type games in which there are a number of non-ordered types in the input, while the output consists of a single real value. When considering the dichotomous case, we extend the Shapley-Shubik power index and provide a full characterization of this extension. Our results generalize the literature on classical cooperative games.

Suggested Citation

  • Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley-Shubik power index for dichotomous multi-type games," Post-Print halshs-01545769, HAL.
    • Handle: RePEc:hal:journl:halshs-01545769
    DOI: 10.1007/s11238-016-9541-4
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01545769
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    References listed on IDEAS

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    1. Edward M. Bolger, 2000. "A consistent value for games with n players and r alternatives," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 93-99.
    2. Tchantcho, Bertrand & Lambo, Lawrence Diffo & Pongou, Roland & Engoulou, Bertrand Mbama, 2008. "Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories," Games and Economic Behavior, Elsevier, vol. 64(1), pages 335-350, September.
    3. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 175-186.
    4. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    5. Dominique Lepelley & N. Andjiga & F. Chantreuil, 2003. "La mesure du pouvoir de vote," Post-Print halshs-00069255, HAL.
    6. R. Amer & F. Carreras & A. Magaña, 1998. "Extension of values to games withmultiple alternatives," Annals of Operations Research, Springer, vol. 84(0), pages 63-78, December.
    7. Bolger, Edward M, 1993. "A Value for Games with n Players and r Alternatives," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(4), pages 319-334.
    8. Annick Laruelle & Federico Valenciano, 2012. "Quaternary dichotomous voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 431-454, March.
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    Citations

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    Cited by:

    1. Aguiar, Victor H. & Pongou, Roland & Tondji, Jean-Baptiste, 2018. "A non-parametric approach to testing the axioms of the Shapley value with limited data," Games and Economic Behavior, Elsevier, vol. 111(C), pages 41-63.
    2. Yuto Ushioda & Masato Tanaka & Tomomi Matsui, 2022. "Monte Carlo Methods for the Shapley–Shubik Power Index," Games, MDPI, vol. 13(3), pages 1-14, June.
    3. Tido Takeng, Rodrigue, 2022. "Uncertain production environment and communication structure," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    4. Josep Freixas & Montserrat Pons, 2021. "On anonymous and weighted voting systems," Theory and Decision, Springer, vol. 91(4), pages 477-491, November.
    5. Courtin, Sébastien, 2022. "Evaluation of decision power in multi-dimensional rules," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 27-36.
    6. Sebastien Courtin & Bertrand Tchantcho, 2019. "Public Good Indices for Games with Several Levels of Approval," Post-Print halshs-02319527, HAL.
    7. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2017. "Dichotomous multi-type games with a coalition structure," Post-Print halshs-01545772, HAL.

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    Keywords

    Game theory; Multi-type games; Simple games; Shapley-Shubik index;
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