We provide a new characterization of the weighted Banzhaf value derived from some postulates in a recent paper by Radzik, Nowak and Driessen [7]. Our approach owes much to the work by Lehrer [4] on the classical Banzhaf value based on the idea of amalgamation of pairs of players and an induction...

We prove that the Banzhaf value is a unique symmetric solution having the dummy player property, the marginal contribution property introduced by Young (1985) and satisfying a very natural reduction axiom of Lehrer (1988).