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Minimal winning coalitions and orders of criticality

Author

Listed:
  • Michele Aleandri

    (Luiss University)

  • Marco Dall’Aglio

    (Luiss University)

  • Vito Fragnelli

    (University of Eastern Piedmont)

  • Stefano Moretti

    (Université PSL)

Abstract

In this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions. The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal. We show that this definition can be formulated referring to the cardinality of the minimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally, we propose to rank all the players lexicographically accounting the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:2:d:10.1007_s10479-021-04199-6
    DOI: 10.1007/s10479-021-04199-6
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    References listed on IDEAS

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