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An axiomatization of the Banzhaf value

Published: 01 June 1988 Publication History

Abstract

An axiomatization of the Banzhaf value is given. It is based on a version of three axioms, which are common to all the semi-values, and on an additional reduction axiom.

References

[1]
Dubey P (1975) On the uniqueness of the Shapley value. International Journal of Game Theory 4:131–139
[2]
Dubey P, Neyman A, Weber RJ (1981) Value theory without efficiency. Math Oper Res 6: 122–128
[3]
Dubey P, Shapley LS (1979) Mathematical properties of the Banzhaf power index. Math Oper Res 4:99–131
[4]
Owen G (1982) Game theory, 2nd ed. Academic Press, New York
[5]
Peleg B (1986) On the reduced game property and its converse. International Journal of Game Theory 15:187–200
[6]
Shapley LS (1953) A value for n-person games. In: Contributions to the theory of games, Annals of Mathematics Studies, vol 28. Princeton Univ. Press, Princeton, pp 307–317
[7]
Sobolev AI (1975) The characterization of optimality principles in cooperative games by functional equations. Mathematical Methods in Social Sciences 6:150–165 [Russian]

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  • (2021)High Dimensional Model ExplanationsProceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency10.1145/3442188.3445903(401-411)Online publication date: 3-Mar-2021
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Published In

cover image International Journal of Game Theory
International Journal of Game Theory  Volume 17, Issue 2
Jun 1988
74 pages

Publisher

Physica-Verlag GmbH

Germany

Publication History

Published: 01 June 1988

Author Tags

  1. Economic Theory
  2. Game Theory
  3. Additional Reduction
  4. Reduction Axiom

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Cited By

View all
  • (2024)Banzhaf Values for Facts in Query AnsweringProceedings of the ACM on Management of Data10.1145/36549262:3(1-26)Online publication date: 30-May-2024
  • (2021)A weighted power distribution mechanism under fuzzy behavior systemsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-19216540:3(3945-3956)Online publication date: 1-Jan-2021
  • (2021)High Dimensional Model ExplanationsProceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency10.1145/3442188.3445903(401-411)Online publication date: 3-Mar-2021
  • (2020)Selection of Information Streams in Social SensingProceedings of the 12th International Conference on Management of Digital EcoSystems10.1145/3415958.3433099(157-161)Online publication date: 2-Nov-2020
  • (2020)Generalized Coleman-Shapley indices and total-power monotonicityInternational Journal of Game Theory10.1007/s00182-019-00692-249:1(299-320)Online publication date: 1-Mar-2020
  • (2019)The Banzhaf Value and General Semivalues for Differentiable Mixed GamesMathematics of Operations Research10.1287/moor.2018.094344:3(767-782)Online publication date: 1-Aug-2019
  • (2019)Analyzing Power in Weighted Voting Games with Super-Increasing WeightsTheory of Computing Systems10.1007/s00224-018-9865-263:1(150-174)Online publication date: 1-Jan-2019
  • (2019)Composition independence in compound games: a characterization of the Banzhaf power index and the Banzhaf valueInternational Journal of Game Theory10.1007/s00182-019-00660-w48:3(755-768)Online publication date: 1-Sep-2019
  • (2018)An Axiomatisation of the Banzhaf Value and Interaction Index for Multichoice GamesModeling Decisions for Artificial Intelligence10.1007/978-3-030-00202-2_12(143-155)Online publication date: 15-Oct-2018
  • (2017)Alternative formulation and dynamic process for the efficient BanzhafOwen indexOperations Research Letters10.1016/j.orl.2016.12.00445:1(60-62)Online publication date: 1-Jan-2017
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