Power Indices and Minimal Winning Coalitions in Simple Games with Externalities

Abstract

We propose a generalization of simple games to sit uations with coalitional externalities. The main novelty of our generalization is a monotonicity property that we define for games in partition function form. This property allows us to properly speak about minimal winning embedded coalitions. We propose and characterize two power indices based on these kind of coalitions. We provide methods based on the multilinear extension of the game to compute the indices. Finally, the new indices are used to study the distribution of power in the current Parliament of Andalusia.