The Shapley value on convex geometries

A game on a convex geometry is a real-valued function defined on the family L of the closed sets of a closure operator which satisfies the finite Minkowski-Krein-Milman property. If L is the boolean algebra 2(N) then we obtain an n-person cooperative game. Faigle and Kern investigated games where L 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. (C) 2000 Elsevier Science B.V. All rights reserved.