Let N be a finite set. By a closure space we mean the family of the closed sets of a closure operator on 2N satisfying the additional condition ∅ = ∅. A simple game on a closure space ℒ is a function υ : ℒ → {0, 1} such that υ(∅) = 0 and υ(N) = 1. We assume simple games are monotonic. The coalitions are the closed sets of ℒ and the players are the elements i ε N. We will give results concerning the structure of the core and the Weber set for this type of games. We show that a simple game is supermodular if and only if the game is a unanimity game and the Core (ℒ, υ) is a stable set if and only if the game υ is a unanimity game.
