Decomposition of Games with Non-empty Core into Veto-Controlled Simple Games

The non-negative games with non-empty core form a polyhedral cone. Extreme directions of this convex cone correspond to veto-controlled simple games. In this paper a constructive method is described to represent a non-negative game with non-empty core as a positive linear combination of veto-controlled simple games. As an application a constructive proof is suggested of a result of spinetto (see [5]) dealing with the extreme points of the compact and convex set of nonnegative (0, 1)-normalized games with non-empty core.