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With a little help from my friends: Essentiality vs opportunity in group criticality

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  • Aleandri, M.
  • Dall’Aglio, M.

Abstract

We define a notion of the criticality of a player for simple monotone games based on cooperation with other players, either to form a winning coalition or to break a winning one, with an essential role for all the players involved. We compare it with the notion of differential criticality given by Beisbart that measures power as the opportunity left by other players.

Suggested Citation

  • Aleandri, M. & Dall’Aglio, M., 2025. "With a little help from my friends: Essentiality vs opportunity in group criticality," Mathematical Social Sciences, Elsevier, vol. 133(C), pages 13-22.
    • Handle: RePEc:eee:matsoc:v:133:y:2025:i:c:p:13-22
    DOI: 10.1016/j.mathsocsci.2024.11.004
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    References listed on IDEAS

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    1. Kjell Hausken & Matthias Mohr, 2001. "The value of a player in n-person games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 465-483.
    2. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    3. Claus Beisbart, 2010. "Groups can make a difference: voting power measures extended," Theory and Decision, Springer, vol. 69(3), pages 469-488, September.
    4. 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.
    5. Marco Dall'Aglio & Vito Fragnelli & Stefano Moretti, 2016. "Orders of criticality in voting games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 53-67.
    6. 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.
    7. M. Aleandri & V. Fragnelli & S. Moretti, 2023. "Lexicographic Ranking Based on Minimal Winning Coalitions," Springer Books, in: Martin A. Leroch & Florian Rupp (ed.), Power and Responsibility, pages 239-256, Springer.
    8. Kjell Hausken, 2020. "The Shapley value of coalitions to other coalitions," Palgrave Communications, Palgrave Macmillan, vol. 7(1), pages 1-10, December.
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