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Indices of Criticality in Simple Games

Author

Listed:
  • Marco Dall’Aglio

    (Department of Economics and Finance, LUISS University, Viale Romania 32, 00197 Roma, Italy)

  • Vito Fragnelli

    (Department of Sciences and Innovative Technologies (DISIT), University of Eastern Piedmont, Viale T. Michel 11, 15121 Alessandria, Italy)

  • Stefano Moretti

    (Université Paris Dauphine, PSL Research University, CNRS, LAMSADE, 75775 Paris, France)

Abstract

Power indices in simple games measure the relevance of a player through her ability in being critical, i.e. essential for a coalition to win. We introduce new indices that measure the power of a player in being decisive through the collaboration of other players. We study the behavior of these criticality indices to compare the power of different players within a single voting situation, and that of the same player with varying weight across different voting situations. In both cases we establish monotonicity results in line with those of Turnovec [1998]. Finally, we examine which properties characterizing the indices of Shapley–Shubik and Banzhaf are shared by these new indices.

Suggested Citation

  • Marco Dall’Aglio & Vito Fragnelli & Stefano Moretti, 2019. "Indices of Criticality in Simple Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-21, March.
    • Handle: RePEc:wsi:igtrxx:v:21:y:2019:i:01:n:s0219198919400036
    DOI: 10.1142/S0219198919400036
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    Cited by:

    1. Michele Aleandri & Marco Dall’Aglio & Vito Fragnelli & Stefano Moretti, 2022. "Minimal winning coalitions and orders of criticality," Annals of Operations Research, Springer, vol. 318(2), pages 787-803, November.
    2. Michele Aleandri & Marco Dall'Aglio, 2022. "With a little help from my friends: essentiality vs opportunity in group criticality," Papers 2207.03565, arXiv.org, revised Feb 2024.

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