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An Axiomatization for Two Power Indices for (3,2)-Simple Games

Author

Listed:
  • Giulia Bernardi

    (Dipartimento di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci, 32, Milano, 20133, Italy)

  • Josep Freixas

    (Departament de Matemà tiques, Escola Politècnica Superior d’Enginyeria de Manresa, Universitat Politècnica de Catalunya, Av. Bases de Manresa, 61–73., Manresa, 08242, Catalunya, Spain)

Abstract

The aim of this work is to give a characterization of the Shapley–Shubik and the Banzhaf power indices for (3,2)-simple games. We generalize to the set of (3,2)-simple games the classical axioms for power indices on simple games: transfer, anonymity, null player property and efficiency. However, these four axioms are not enough to uniquely characterize the Shapley–Shubik index for (3,2)-simple games. Thus, we introduce a new axiom to prove the uniqueness of the extension of the Shapley–Shubik power index in this context. Moreover, we provide an analogous characterization for the Banzhaf index for (3,2)-simple games, generalizing the four axioms for simple games and adding another property.

Suggested Citation

  • Giulia Bernardi & Josep Freixas, 2019. "An Axiomatization for Two Power Indices for (3,2)-Simple Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-24, March.
    • Handle: RePEc:wsi:igtrxx:v:21:y:2019:i:01:n:s0219198919400012
    DOI: 10.1142/S0219198919400012
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    Cited by:

    1. Josep Freixas, 2020. "The Banzhaf Value for Cooperative and Simple Multichoice Games," Group Decision and Negotiation, Springer, vol. 29(1), pages 61-74, February.

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