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• Gerard van der Laan

An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms.

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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 15 (1998)
Issue (Month): 4 ()
Pages: 567-582
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Handle: RePEc:spr:sochwe:v:15:y:1998:i:4:p:567-582

Note: Received: 10 April 1996 / Accepted: 2 June 1997
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   Other versions:
   • Brink, R. van den & Laan, G. van der, 2001. "A class of consistent share functions for games in coalition structure," Discussion Paper 33, Tilburg University, Center for Economic Research. [Downloadable!]
   • van den Brink, Rene & van der Laan, Gerard, 2005. "A class of consistent share functions for games in coalition structure," Games and Economic Behavior, Elsevier, vol. 51(1), pages 193-212, April. [Downloadable!] (restricted)
5. Brink, R. van den & Laan, G. van der, 1999. "Core concepts for share vectors," Discussion Paper 64, Tilburg University, Center for Economic Research. [Downloadable!]
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6. Brink, R. van den & Laan, G. van der, 1999. "Potentials and reduced games for share functions," Discussion Paper 41, Tilburg University, Center for Economic Research. [Downloadable!]
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7. Brink, R. van den, 1999. "An axiomatization of the shapley value using a fairness property," Discussion Paper 120, Tilburg University, Center for Economic Research. [Downloadable!]
8. René van den Brink & Yukihiko Funaki & Yuan Ju, 2007. "Consistency, Monotonicity and Implementation of Egalitarian Shapley Values," Tinbergen Institute Discussion Papers 07-062/1, Tinbergen Institute. [Downloadable!]
9. Annick Laruelle, 1999. "- On The Choice Of A Power Index," Working Papers. Serie AD 1999-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
10. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2003. "Harsanyi Solutions in Line-graph Games," Tinbergen Institute Discussion Papers 03-076/1, Tinbergen Institute. [Downloadable!]

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