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note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom


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  • Andrzej S. Nowak

    (Institute of Mathematics, Technical University of Wroclaw, 50-370 Wroclaw, Poland)


We prove that the Banzhaf value is a unique symmetric solution having the dummy player property, the marginal contribution property introduced by Young (1985) and satisfying a very natural reduction axiom of Lehrer (1988).

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 26 (1997)
Issue (Month): 1 ()
Pages: 137-141

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Handle: RePEc:spr:jogath:v:26:y:1997:i:1:p:137-141

Note: Received January 1996 Revised version July 1996
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Cited by:
  1. Marcin Malawski, 2002. "Equal treatment, symmetry and Banzhaf value axiomatizations," International Journal of Game Theory, Springer, vol. 31(1), pages 47-67.
  2. André Casajus, 2011. "Marginality, differential marginality, and the Banzhaf value," Theory and Decision, Springer, vol. 71(3), pages 365-372, September.
  3. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali, 2006. "On the Coleman indices of voting power," European Journal of Operational Research, Elsevier, vol. 171(1), pages 273-289, May.
  4. Yan-An Hwang & Yu-Hsien Liao, 2010. "Consistency and dynamic approach of indexes," Social Choice and Welfare, Springer, vol. 34(4), pages 679-694, April.
  5. Lucia Pusillo, 2013. "Banzhaf LikeValue for Games with Interval Uncertainty," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 7(1), pages 005-014, March.
  6. Brink, J.R. van den & Laan, G. van der, 2001. "A Class of Consistent Share Functions For Games in Coalition Structure," Discussion Paper 2001-33, Tilburg University, Center for Economic Research.
  7. Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD 2000-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. Mikel Álvarez-Mozos & Oriol Tejada Pinyol, 2014. "The Banzhaf Value in the Presence of Externalities," UB Economics Working Papers 2014/302, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
  9. Tadeusz Radzik & Andrzej Nowak & Theo Driessen, 1997. "Weighted Banzhaf values," Computational Statistics, Springer, vol. 45(1), pages 109-118, February.
  10. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali & Sarka, Palash, 2007. "A Characterization and Some Properties of the Banzhaf-Coleman-Dubey-Shapley Sensitivity Index," Staff General Research Papers 12807, Iowa State University, Department of Economics.
  11. André Casajus, 2012. "Amalgamating players, symmetry, and the Banzhaf value," International Journal of Game Theory, Springer, vol. 41(3), pages 497-515, August.
  12. Gerard van der Laan & René van den Brink, 2002. "A Banzhaf share function for cooperative games in coalition structure," Theory and Decision, Springer, vol. 53(1), pages 61-86, August.
  13. André Casajus, 2014. "Collusion, quarrel, and the Banzhaf value," International Journal of Game Theory, Springer, vol. 43(1), pages 1-11, February.


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