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Dichotomous multi-type games with a coalition structure

Author

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  • Sébastien Courtin

    () (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - 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

    () (ENSP - Ecole Nationale Supérieure Polytechnique [Yaoundé] - Université de Yaoundé I [Yaoundé])

Abstract

This work focuses on the evaluation of voting power in dichotomous multi-type games endowed with a coalition structure. Dichotomous multi-type games, introduced by Courtin et al. [2016], model games in which there is a number of non-ordered types of support in the input, while the output is dichotomous, i.e. the proposal is either accepted or rejected. In a game with a coalition structure, it is supposed that players organize themselves into disjoint coalitions wich are defined a priori. We extend the well-known Owen index (Owen [1977]) and Banzhaf-Owen index (Owen [1981]) to this class of games. A full characterization of these power indices is provided.

Suggested Citation

  • Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2017. "Dichotomous multi-type games with a coalition structure," Post-Print halshs-01545772, HAL.
  • Handle: RePEc:hal:journl:halshs-01545772
    DOI: 10.1016/j.mathsocsci.2016.12.003
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01545772
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    File URL: https://halshs.archives-ouvertes.fr/halshs-01545772/document
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    References listed on IDEAS

    as
    1. Sébastien Courtin & Bertrand Tchantcho, 2015. "A note on the ordinal equivalence of power indices in games with coalition structure," Theory and Decision, Springer, vol. 78(4), pages 617-628, April.
    2. 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.
    3. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, December.
    4. 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.
    5. repec:hal:journl:halshs-00178916 is not listed on IDEAS
    6. Albizuri, M.J. & Aurrecoechea, J. & Zarzuelo, J.M., 2006. "Configuration values: Extensions of the coalitional Owen value," Games and Economic Behavior, Elsevier, vol. 57(1), pages 1-17, October.
    7. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 399-431, December.
    8. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 153-167, February.
    9. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley–Shubik power index for dichotomous multi-type games," Theory and Decision, Springer, vol. 81(3), pages 413-426, September.
    10. M. Albizuri & José Zarzuelo, 2000. "Coalitional values for cooperative games withr alternatives," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-30, June.
    11. repec:spr:compst:v:65:y:2007:i:1:p:153-167 is not listed on IDEAS
    12. 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.
    13. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    14. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley-Shubik power index for dichotomous multi-type games," Post-Print halshs-01545769, HAL.
    15. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    16. 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.
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    Cited by:

    1. Sebastien Courtin & Bertrand Tchantcho, 2019. "Public Good Indices for Games with Several Levels of Approval," Post-Print halshs-02319527, HAL.

    More about this item

    Keywords

    Banzhaf-Owen power index; Owen power index; Coalition structure; Dichotomous multi-type games;

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