Characteristic function representation of n-person cooperative games precludes the modeling of structural properties of a game other than the relationship between coalition structure and the worth of a game. This means that the Shapley value, a measure of expected return to a player from playing the game, is restricted as a solution concept to only those games satisfying the condition that all coalitions of the same cardinality are equiprobable. By contrast, as we demonstrate below, Shapley's three axioms are satisfied for Shapley-like measures based on richer characterizations of a game. In particular, we extend the Shapley value to a class of abstract games for which the roles that players assume are determinants of the likelihood of particular coalitions and for which the original Shapley value can be found as a special case
