A game on a convex geometry is a real-valued function defined on the family of the closed sets of a closure operator which satisfies the finite Minkowski–Krein–Milman property. If is the boolean algebra 2N then we obtain an n-person cooperative game. Faigle and Kern investigated games where is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axioms that give rise to a unique Shapley value for games on convex geometries.