Coalition values and generalized characteristic functions

We study coalitional values for games in generalized characteristic function form. There are two extensions of the Shapley value in this context, one introduced by Nowak and Radzik and the other introduced by us. We generalize both values to games with a priori unions in the same way that Owen did for the Shapley value, and we obtain an axiomatic characterization for both of them. Moreover we analyze the differences between them and study the consistency, the balanced contributions, and the potential.