Extension of values to games with multiple alternatives

Games with multiple alternatives enlarge the domain of social situations mo delled by the classical cooperative game theory. In this paper, we prove th at any linear value defined for traditional cooperative games admits a natu ral extension to games with multiple alternatives. A method to compute the extended values is also provided. As specific examples, we present an appli cation of the Shapley value and the Banzhaf-Coleman index to two voting sit uations taken from the real world.