Power indices and minimal winning coalitions for simple games in partition function form

Abstract

We propose a generalization of simple games to partition function form games based on a monotonicity property that we define in this context. This property allows us to properly speak about minimal winning embedded coalitions. We propose and characterize two power indices based on such coalitions. Finally, the new indices are used to study the distribution of power in the Parliament of Andalusia that emerged after the elections of March 22, 2015.