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Extension of values to games withmultiple alternatives

Author

Listed:
  • R. Amer
  • F. Carreras
  • A. Magaña

Abstract

Games with multiple alternatives enlarge the domain of social situations modelled by the classical cooperative game theory. In this paper, we prove that any linear value defined for traditional cooperative games admits a natural extension to games with multiple alternatives. A method to compute the extended values is also provided. As specific examples, we present an application of the Shapley value and the Banzhaf-Coleman index to two voting situations taken from the real world. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:84:y:1998:i:0:p:63-78:10.1023/a:1018901306738
    DOI: 10.1023/A:1018901306738
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    Citations

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    Cited by:

    1. 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.
    2. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    3. Francesc Carreras & Antonio Magaña, 2008. "The Shapley–Shubik index for simple games with multiple alternatives," Annals of Operations Research, Springer, vol. 158(1), pages 81-97, February.
    4. Luisa Monroy & Francisco Fernández, 2014. "Banzhaf index for multiple voting systems. An application to the European Union," Annals of Operations Research, Springer, vol. 215(1), pages 215-230, April.
    5. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley-Shubik power index for dichotomous multi-type games," Post-Print halshs-01545769, HAL.
    6. Josep Freixas & Montserrat Pons, 2022. "A critical analysis on the notion of power," Annals of Operations Research, Springer, vol. 318(2), pages 911-933, November.
    7. Sascha Kurz & Issofa Moyouwou & Hilaire Touyem, 2021. "Axiomatizations for the Shapley–Shubik power index for games with several levels of approval in the input and output," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 569-594, April.
    8. Courtin, Sébastien & Nganmeni, Zéphirin & Tchantcho, Bertrand, 2017. "Dichotomous multi-type games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 9-17.
    9. Luisa Monroy & Francisco Fernández, 2012. "Stable sets and cores for multi-criteria simple games and for their extensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 1-22, June.
    10. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2020. "Weighted committee games," European Journal of Operational Research, Elsevier, vol. 282(3), pages 972-979.
    11. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2017. "Dichotomous multi-type games with a coalition structure," Post-Print halshs-01545772, HAL.
    12. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(C).
    13. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.
    14. Sébastien Courtin & Zephirin Nganmeni & Bertrand Tchantcho, 2015. "Dichotomous multi-type games: Shapley-Shubik and Banzhaf-Coleman power indices," THEMA Working Papers 2015-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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