A characterization of the Shapley value for cooperative games with fuzzy characteristic function

Abstract

The characteristic function of a cooperative game determines the payment that each coalition can obtain when the players in the coalition cooperate. But there are cooperative situations in which the players have only imprecise expectations about the profit that can be achieved by each coalition. These situations are modeled through cooperative games with fuzzy characteristic function, in which the payment of each coalition is a fuzzy quantity. A value for these games assigns to each player in a game a fuzzy quantity that indicates the vaguely expected payoff for the player. There is a Shapley value for games with fuzzy characteristic function, but no characterization of this value has been given in the literature. In this paper a characterization of the Shapley value for games with fuzzy characteristic function is presented.