Simple games on closure spaces

Let N be a ...nite set. By a closure space we mean the family of the closed sets of a closure operator on 2 satisfying the additional condition ; = ;. A simple game on a closure space L is a function v : L ! f0; 1g such that v(;) = 0 and v (N) = 1. We assume simple games are monotonic. The coalitions are the closed sets of L and the players are the elements i 2 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; v) is a stable set if and only if the game v is a unanimity game.