The consistent value of fuzzy games

In the framework of fuzzy games, we offer an extension of the reduced game introduced by Hart and Mas-Colell, which we name the self-reduced game. According to consistency which related to the self-reduced game, we provide a definition of the consistent value which is a generalization of the Shapley value of fuzzy games. We adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games. The first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value. Second, based on the properties of balanced contributions and consistency, we offer several axiomatizations of the consistent value. Finally, we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments.