Extension of values to games withmultiple alternatives

Abstract

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