A Banzhaf Function for a Fuzzy Game

In this paper, another important solution for fuzzy games, called the Banzhaf function, is investigated. First, a simplified expression for the Banzhaf function for games with fuzzy coalition is proposed. The relationship between this simplified expression and two kinds of particular Banzhaf functions are discussed in detail. Furthermore, in the framework of games with fuzzy coalitions, we give a definition of the potential function of fuzzy games, and prove that the marginal values of the potential function are the components of the Banzhaf function. Furthermore, a new axiomatic characterization of the Banzhaf function for games with fuzzy coalitions is provided.