Some properties of the core on convex geometries

A game on a convex geometry was introduced by Bilbao as a model of partial cooperation. We investigate some properties of the core of a game on a convex geometry. First, we show that if a game is quasi-convex, then the core is stable. This result can be seen as an extension of a result by Shapley for traditional cooperative games. Secondly, we show the core on the class of balanced games on a convex geometry has a consistency property, called the reduced game property. Moreover, we axiomatize the core by means of consistency, as is analogous to a result by Peleg for traditional cooperative games.