Dichotomous multi-type games with a coalition structure

This work focuses on the evaluation of voting power in dichotomous multi-type games endowed with a coalition structure. Dichotomous multi-type games, introduced by Courtin et al. (2016), model games in which there is a number of non-ordered types of support in the input, while the output is dichotomous, i.e. the proposal is either accepted or rejected. In a game with a coalition structure, it is supposed that players organize themselves into disjoint coalitions which are defined a priori. We extend the well-known Owen index and Banzhaf-Owen index to this class of games. A full characterization of these power indices is provided.