International Journal of Game Theory

, Volume 11, Issue 1, pp 1–12 | Cite as

Characterizing the Banzhaf and Shapley values assuming limited linearity

  • E. M. Bolger


This paper presents characterizations of the Banzhaf-Coleman and Shapley-Shubik indices for monotonic simple games. The characterizations are obtained without explicitly requiring that the indices satisfy the linearity assumptionψ (v∧ w) +ψ (v ∨ w) =ψ (v) + ψ (w). The ideas developed are then used to obtain a characterization of the Banzhaf value for the class of alln-person games in characteristic function form.


Characteristic Function Economic Theory Game Theory Function Form Simple Game 
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Copyright information

© Physica-Verlag Ges.m.b.H 1982

Authors and Affiliations

  • E. M. Bolger
    • 1
  1. 1.Department of Mathematics and StatisticsMiami UniversityOxfordUSA

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