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Weighted Banzhaf values

Author

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  • Tadeusz Radzik
  • Andrzej Nowak
  • Theo Driessen

Abstract

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values. Copyright Physica-Verlag 1997

Suggested Citation

  • Tadeusz Radzik & Andrzej Nowak & Theo Driessen, 1997. "Weighted Banzhaf values," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 109-118, February.
    • Handle: RePEc:spr:mathme:v:45:y:1997:i:1:p:109-118
    DOI: 10.1007/BF01194250
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    References listed on IDEAS

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    1. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    2. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    3. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    4. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
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    Cited by:

    1. Conrado M. Manuel & Daniel Martín, 2021. "A Monotonic Weighted Banzhaf Value for Voting Games," Mathematics, MDPI, vol. 9(12), pages 1-23, June.
    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. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.

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