A simple game is a game in coalitional form, with transferable utility, such that v(N) = 1, where N is the grand coalition of all players, v({i}) = 0 for every player i in N, and, for each other coalition S, v(S) equals either 0 or 1. Player i is a veto player for a simple game v iff
u(S) = 0, ∀S ⊆ N - i
Show that the core of any simple game can be characterized in terms of its set of veto players.
(HINT: Your characterization should imply that the core is empty if there are no veto players.)