Abstract
We provide new, concise characterizations of the Banzhaf value on a fixed player set employing just the standard dummy player property and one of the collusion properties suggested by Haller (Int J Game Theory 23:261–281, 1994) and Malawski (Int J Game Theory 31:47–67, 2002). Within these characterizations, any of the collusion properties can be replaced by additivity and the quarrel property due to the latter author.
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References
Alonso-Meijide JM, lvarez-Mozos M, Fiestras-Janeiro MG (2012) Notes on a comment on 2-efficiency and the Banzhaf value. Appl Math Lett 25(7):1098–1100
Banzhaf JF (1965) Weighted voting does not work: a mathematical analysis. Rutgers Law Rev 19:317–343
Casajus A (2010) Amalgamating players, symmetry, and the Banzhaf value. Working paper 442. IMW Institute of Mathematical Economics, Bielefeld University, Germany
Casajus A (2011) Marginality, differential marginality, and the Banzhaf value. Theory Decis 71(3):365–372
Casajus A (2012) Amalgamating players, symmetry, and the Banzhaf value. Int J Game Theory 41(3): 497–515
Dubey P, Einy E, Haimanko O (2005) Compound voting and the Banzhaf index. Games Econ Behav 51:20–30
Feltkamp V (1995) Alternative axiomatic characterizations of the Shapley and the Banzhaf values. Int J Game Theory 24:179–186
Haller H (1994) Collusion properties of values. Int J Game Theory 23:261–281
Laruelle A, Valenciano F (2001) Shapley-Shubik and Banzhaf indices revisited. Math Oper Res 26(1): 89–104
Lehrer E (1988) An axiomatization of the Banzhaf value. Int J Game Theory 17(2):89–99
Malawski M (2002) Equal treatment, symmetry and Banzhaf value axiomatizations. Int J Game Theory 31:47–67
Nowak AS (1997) On an axiomatization of the Banzhaf value without the additivity axiom. Int J Game Theory 26:137–141
Owen G (1975) Multilinear extensions and the Banzhaf value. Naval Res Logist Q 22:741–750
Shapley LS (1953) A value for \(n\)-person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games, vol II. Princeton University Press, Princeton, pp 307–317
Young HP (1985) Monotonic solutions of cooperative games. Int J Game Theory 14:65–72
Acknowledgments
We are indebted to Frank Huettner for helpful discussions on the matter.
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Casajus, A. Collusion, quarrel, and the Banzhaf value. Int J Game Theory 43, 1–11 (2014). https://doi.org/10.1007/s00182-012-0364-4
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DOI: https://doi.org/10.1007/s00182-012-0364-4