An axiomatization of the Banzhaf value
The Banzhaf value was originally given by an axiomatization. In Owen's book the axiomatization of Banzhaf's value is based on the tool of the compound game and is not determined uniquely. Another axiomatization given by Dubey and Shapley employs a different approach. It is based on four axioms, three of them are standard and in fact determine the semi- value. The author here adopts these three axioms, then replaces the fourth axiom of Dubey and Shapley by some reduction axiom, which has an intuitive meaning. This axiom says something about the value of the game in terms of another game, with a smaller number of players. The author defines for each coalition T two T-games derived from the original game by amalgamating all the players of T to one player called \(\bar T.\) His additional axiom says that for any two-player-coalition \(T=\{i,j\}\) the sum of the values of i and of j in the original game is less or equal to the value of T in the \(\bar T-\)game. According to this axioms a unification of any two players is profitable.
scientific article; zbMATH DE number 4062865