Characterization of the Banzhaf value using a consistency axiom - Sánchez P., Joss (CUBO, A Mathematical Journal, 2010)
One of the important properties characterizing cooperative game solutions is consistency. This notion establishes connections between the solution vectors of a cooperative game and those of its reduced game. The last one is obtained from the initial game by removing one or more players and by giving them payoffs according to a specific principle. Consistency of a solution means that the restriction of a solution payoff vector of the initial game to any coalition belongs to the solution set of the corresponding reduced game. In this paper, we show that the Banzhaf value is consistent with respect to a suitable reduced game. We also show that consistency together with standardness for two-person games characterize the Banzhaf value.