An intersection theorem in TU cooperative game theory

We prove a theorem on the intersection of the Weber sets (Weber, 1988) of two ordered cooperative games. From this theorem several consequences are derived, the inclusion of the core in the Weber set (Weber, 1988), the fact that every convex game has a large core (Sharkey, 1982), and a discrete separation theorem (Frank, 1982). We introduce a definition of general largeness, proving that the Weber set is large for any cooperative game.