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note: An alternative characterization of the weighted Banzhaf value

Author

Listed:
  • Andrzej S. Nowak

    (Institute of Mathematics, Technical University of Zielona GÕra, PodgÕrna 50, 65-246 Zielona GÕra, Poland Institute of Mathematics, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland)

  • Tadeusz Radzik

    (Institute of Mathematics, Technical University of Zielona GÕra, PodgÕrna 50, 65-246 Zielona GÕra, Poland Institute of Mathematics, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland)

Abstract

We provide a new characterization of the weighted Banzhaf value derived from some postulates in a recent paper by Radzik, Nowak and Driessen [7]. Our approach owes much to the work by Lehrer [4] on the classical Banzhaf value based on the idea of amalgamation of pairs of players and an induction construction of the value. Compared with the approach in [7] we consider two new postulates: a weighted version of Lehrer's "2-efficiency axiom" [4] and a generalized "null player out" property studied in terms of symmetric games by Derks and Haller [2].

Suggested Citation

  • Andrzej S. Nowak & Tadeusz Radzik, 2000. "note: An alternative characterization of the weighted Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 127-132.
    • Handle: RePEc:spr:jogath:v:29:y:2000:i:1:p:127-132
    Note: Received: December 1997/final version: October 1999
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    Citations

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    Cited by:

    1. 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.
    2. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    3. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
    4. Barua, Rana & Chakravarty, Satya R. & Sarkar, Palash, 2009. "Minimal-axiom characterizations of the Coleman and Banzhaf indices of voting power," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 367-375, November.

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