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On the consistency of the Banzhaf semivalue

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Abstract

In this note we show that the Banzhaf semivalue is consistent with respect to a suitable reduced game which keeps a clear parallelism with that defined by Hart and Mas-Colell in (1989) to prove the consistency of the Shapley value. We also use this reduced game property to characterize the Banzhaf semivalue.

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References

  • Banzhaf J. F. 1965. Weighted voting doesn't work: a mathematical analysis.Rutgers Law Review 19, 317–343.

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  • Hart S. and Mas-Colell A. 1989. Potential, Value and Consistency,Econometrica 57, 589–614.

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  1. Dto. Economía Aplicada I, Facultad de Ciencias Económicas, Universidad del Pais Vasco, Avenida Lehendakari Aguirre, 83, 48015, Bilbao, Spain

    Luis M. Ruiz

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  1. Luis M. Ruiz
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Ruiz, L.M. On the consistency of the Banzhaf semivalue. Top 7, 163–168 (1999). https://doi.org/10.1007/BF02564718

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  • DOI: https://doi.org/10.1007/BF02564718

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