We follow the path initiated in Shapley (1971) and study the geometry of the core of convex and strictly convex games. We define what we call face games and use them to study the combinatorial complexity of the core of a strictly convex game. Remarkably, we present a picture that summarizes our results with the aid of Pascal’s triangle. JEL classification: C71.

We consider TU-games with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. In such a situation, the core may be unbounded, and one has to select a bounded part of the core as a solution concept. The restricted core is obtained by imposing equality constraints in the core for sets belonging to so-cal...

In a geometric drawing of Kn, trivially each 3-cycle bounds convex region: if two vertices are in that region, then so is the (geometric) edge between them. We define topological D Kn to be closed region R such any have (topological) them contained R.While drawings generalize drawings, they specialize ones. Therefore it might surprising all optimal (that is, crossing-minimal) were convex. Howev...