Theory and Decision

, Volume 71, Issue 3, pp 365-372

First online:

Marginality, differential marginality, and the Banzhaf value

  • André CasajusAffiliated withLSI Leipziger Spieltheoretisches InstitutIMW Institute of Mathematical Economics, Bielefeld UniversityChair of Economics and Information Systems, HHL Leipzig Graduate School of ManagementWirtschaftswissenschaftliche Fakultät, Universität Leipzig Email author 

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We revisit the Nowak (Int J Game Theory 26:137–141, 1997) characterization of the Banzhaf value via 2-efficiency, the Dummy player axiom, symmetry, and marginality. In particular, we provide a brief proof that also works within the classes of superadditive games and of simple games. Within the intersection of these classes, one even can drop marginality. Further, we show that marginality and symmetry can be replaced by van den Brink fairness/differential marginality. For this axiomatization, 2-efficiency can be relaxed into superadditivity on the full domain of games.


Banzhaf value Additivity Marginality Differential marginality

JEL Classification