Decomposition of games with non-empty core into veto-controlled simple games (Q580201)

The non-negative games with non-empty core form a polyhedral cone. The 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 \textit{R. Spinetto} [Manage. Sci., Theory 20, 1292-1299 (1974; Zbl 0314.90103)] dealing with the extreme points of the compact and convex set of nonnegative (0,1)- normalized games with non-empty core.