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New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property

TOP volume 25, pages 579–600 (2017)Cite this article

Abstract

In this paper, several characterizations of the Owen and the Banzhaf–Owen values are provided. All the characterizations make use of a property based on the principle of balanced contributions. This property is called the intracoalitional balanced contributions property and was defined by Calvo et al. (Math Soc Sci 31:171–182, 1996).

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Notes

  1. Given a TU-game (N, v), \(P_{Sh}(N,v)={\sum _{S\subseteq N}}\frac{(s-1)!(n-s)!}{n!}v(S)\).

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Acknowledgements

Financial support from Ministerio de Ciencia y Tecnología through Grant ECO2011-23460 and from Ministerio de Economía y Competitividad through Grant MTM2014-53395-C3-1-P is gratefully acknowledged. Partial support from Xunta de Galicia through Grants ED431G/012016-2019 and ED431C2016-015 is gratefully acknowledged. I am also very grateful for the interesting comments of two anonymous referees.

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Authors and Affiliations

  1. MODES Research Group, Department of Mathematics, Faculty of Computer Science, Universidade da Coruña, 15071, A Coruña, Spain

    Silvia Lorenzo-Freire

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  1. Silvia Lorenzo-Freire
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Correspondence to Silvia Lorenzo-Freire.

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Lorenzo-Freire, S. New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property. TOP 25, 579–600 (2017). https://doi.org/10.1007/s11750-017-0446-3

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Keywords

  • Cooperative game
  • Shapley value
  • Banzhaf value
  • Coalition structure
  • Balanced contributions

Mathematics Subject Classification

  • 91A12