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Reformulation of Some Indices Using Null Player Free Winning Coalitions

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Transactions on Computational Collective Intelligence XXXVI

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 13010))

Abstract

The proposal of this paper is a new representation for some power indices in a simple game using null player free winning coalitions. Analogously to a set of winning coalitions and minimal winning coalitions, a set of null player free winning coalitions fully captures the characteristics of a simple game. Moreover, expressing indices by winning coalitions that do not contain null players allows us to show the parts of the power that are assigned to null and non-null players in a simple game in a transparent manner.

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Author information

Authors and Affiliations

  1. AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Krakow, Poland

    Izabella Stach

  2. Department of Economics, University of Bergamo, Via dei Caniana, 2, 24127, Bergamo, Italy

    Cesarino Bertini

Authors
  1. Izabella Stach
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  2. Cesarino Bertini
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Corresponding author

Correspondence to Izabella Stach .

Editor information

Editors and Affiliations

  1. Wroclaw University of Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

  2. Swinburne University of Technology, Hawthorn, VIC, Australia

    Ryszard Kowalczyk

  3. WSB University Wroclaw, Wroclaw, Poland

    Anna Motylska-Kuźma

  4. WSB University Wroclaw, Wroclaw, Poland

    Jacek Mercik

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Stach, I., Bertini, C. (2021). Reformulation of Some Indices Using Null Player Free Winning Coalitions. In: Nguyen, N.T., Kowalczyk, R., Motylska-Kuźma, A., Mercik, J. (eds) Transactions on Computational Collective Intelligence XXXVI. Lecture Notes in Computer Science(), vol 13010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-64563-5_6

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  • DOI: https://doi.org/10.1007/978-3-662-64563-5_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-64562-8

  • Online ISBN: 978-3-662-64563-5

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