• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2022, Volume: 15, Issue: 40, Pages: 2077-2084

Original Article

Consolidation of an Efficient and a Non-Efficient Solution in a Cooperative Game: The Egalitarian Banzhaf Value

Received Date:25 May 2022, Accepted Date:10 September 2022, Published Date:29 October 2022


Objective: The principles of marginalism and egalitarianism are handy tools for sharing worth among the players of a group in a TU game. Here, our objective is to combine two such solutions to generate a new value that keeps in mind the need of each player required for the survival of a group in a TU game. Methods: Here, the Banzhaf value and the equal division value were merged to establish a new consolidated solution. Method of induction is used over unanimity games and symmetric games to characterize the proposed value using some well-known as well as some freshly defined axioms of cooperative game theory. Findings: To describe the new value, we first looked at a number of intuitive axioms linked to it and the uniqueness of the value is obtained by characterizing it using the defined axioms. The value is then extended to the class of simple games. Novelty: The proposed solution is a non-efficient solution that allocates a portion of the total worth to the players and keeps a portion undistributed to use for the purpose of further investment by the group.

Keywords: Cooperative game; Banzhaf value; Egalitarian Value; Null Player; Solution Concept


  1. Banzhaf JFI. Weighted voting does not work: A mathematical analysis. Rutgers Law Review. 1965;19:317–343.
  2. Li DF, Ye YF, Fei W. Extension of generalized solidarity values to interval-valued cooperative games. Journal of Industrial & Management Optimization. 2020;16(2):919–931. Available from: https://doi.org/10.3934/jimo.2018185
  3. Dubey P, Neyman A, Weber RJ. Value Theory Without Efficiency. Mathematics of Operations Research. 1981;6(1):122–128. Available from: https://doi.org/10.1287/moor.6.1.122
  4. Gallego I, Fernández JR, Jiménez-Losada A, Ordóñez M. A Symmetric Banzhaf Cooperation Value for Games with a Proximity Relation among the Agents. Symmetry. 2020;12(7):1196. Available from: https://doi.org/10.3390/sym12071196
  5. Choudhury D, Borkotokey S, Kumar R, Sarangi S. The Egalitarian Shapley value: a generalization based on coalition sizes. Annals of Operations Research. 2021;301(1-2):55–63. Available from: https://doi.org/10.1007/s10479-020-03675-9
  6. Choudhary D, Borkotokey S, Kumar R, Sarangi S. Consolidating Marginalism and Egalitarianism: A New value Transferable utility games. SSRN Electronic Journal. 2020. Available from: https://doi.org/10.2139/ssrn.3729927
  7. Lehrer E. An axiomatization of the Banzhaf value. International Journal of Game Theory. 1988;17(2):89–99. Available from: https://doi.org/10.1007/bf01254541


© 2022 Bora et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


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