Reformulation of Some Indices Using Null Player Free Winning Coalitions

The proposal of this paper is a new representation for some power indices in a simple game using null player free winning coalitions. Analogously to a set of winning coalitions and minimal winning coalitions, a set of null player free winning coalitions fully captures the characteristics of a simple game. Moreover, expressing indices by winning coalitions that do not contain null players allows us to show the parts of the power that are assigned to null and non-null players in a simple game in a transparent manner.