Probabilistic values 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 Mink owski-Krein-Milman property. If L is the Boolean algebra 2(N), then we obta in an n-person cooperative game. We will extend the work of Weber on probab ilistic values to games on convex geometries. As a result, we obtain a fami ly of axioms that give rise to several probabilistic values and a unique Sh apley value for games on convex geometries.