The Nakamura number is an appropriate invariant of a simple game in order to study the existence of social equilibria and the possibility of cycles. For symmetric quota games its number can be obtained by an easy formula. For some subclasses of simple games the corresponding Nakamura number has...

The study of the characterization of threshold functions within the class of switching functions is an important problem that goes back at least to the mid-20th century. Due to different motivations switching and threshold functions have been investigated in a variety of different mathematical...

We study minimum integer representations of weighted games, i.e. representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if the exist at all, are linked with some solution concepts in...

This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class as well. Second, we focus on the special case of...

Manfred Holler introduced the Public Good index as a proposal to divide a public good among players. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining...