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On the externality-free Shapley–Shubik index

Author

Listed:
  • Álvarez-Mozos, M.
  • Alonso-Meijide, J.M.
  • Fiestras-Janeiro, M.G.

Abstract

We address the problem of extending the Shapley–Shubik index to the class of simple games with externalities introduced in Alonso-Meijide et al. (2017). On the one hand, we provide bounds for any efficient, symmetric, and monotonic power index. On the other hand, we characterize the restriction of the externality-free value of de Clippel and Serrano (2008) to the class of games under study by adapting well-known properties.

Suggested Citation

  • Álvarez-Mozos, M. & Alonso-Meijide, J.M. & Fiestras-Janeiro, M.G., 2017. "On the externality-free Shapley–Shubik index," Games and Economic Behavior, Elsevier, vol. 105(C), pages 148-154.
    • Handle: RePEc:eee:gamebe:v:105:y:2017:i:c:p:148-154
    DOI: 10.1016/j.geb.2017.07.009
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    References listed on IDEAS

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    1. Dutta, Bhaskar & Ehlers, Lars & Kar, Anirban, 2010. "Externalities, potential, value and consistency," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2380-2411, November.
    2. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
    3. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    4. McQuillin, Ben, 2009. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," Journal of Economic Theory, Elsevier, vol. 144(2), pages 696-721, March.
    5. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    6. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
    7. 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.
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    Cited by:

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    2. Gusev, Vasily V., 2020. "The vertex cover game: Application to transport networks," Omega, Elsevier, vol. 97(C).
    3. Albizuri, M.J. & Goikoetxea, A., 2022. "Probabilistic Owen-Shapley spatial power indices," Games and Economic Behavior, Elsevier, vol. 136(C), pages 524-541.
    4. G. Arévalo-Iglesias & M. Álvarez-Mozos, 2020. "Power distribution in the Basque Parliament using games with externalities," Theory and Decision, Springer, vol. 89(2), pages 157-178, September.

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    More about this item

    Keywords

    Externality-free value; Shapley–Shubik index; Partition function;
    All these keywords.

    JEL classification:

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

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