A characterization of cooperative TU-games with large monotonic core

Cooperative TU-games with large core were introduced by Sharkey (1982) and the concept of Population Monotonic Allocation Scheme was defined by Sprumont (1990). Linking these two concepts, Moulin (1990) introduces the notion of large monotonic core giving a characterization for three-player games. In this paper we prove that all games with large monotonic core are convex. We give an effective criterion to determine whether a game has large monotonic core and, as a consequence, we obtain a characterization for the four-player case.