On the Notion of Dimension and Codimension of Simple Games

This paper presents novel concept of a dimension and codimension for the class of simple games. It introduces a dual concept of a dimension which is obtained by considering the union instead of the intersection as the basic operation, and several other extensions of the notion of dimension. It also shows the existence and uniqueness of a minimum subclasses of games, with the property that every simple game can be expressed as an intersection, or respectively, the union of them. We show the importance of these subclasses in the description of a simple game, and give a practical interpretation of them.