Dichotomous multi-type games with a coalition structure

This work focuses on the evaluation of the voting power in dichotomous multi-type games endowed with a coalition structure (DMGCs). Dichotomous multi-type games have been introduced by Courtin et al. [2015] in order to generalize simple game. They modelize game in which there are a number of non-ordered types of support in the input, while the output is dichotomous, i.e. the proposal is accepted or rejected. In game with a coalition structure it is supposed that players organize themselves into a priori disjoint coalitions. We extend the well known Owen-Shapley index (Owen [1977]) and Owen-Banzhaf index (Owen [1981]) to DMGCs. A full characterization of these power indices are provided.