Core and monotonic allocation methods

Young showed in a paper of 1985 (Int. J. Game Theory 14, 65-72) that no cor e allocation method can be coalitionally monotonic on cooperative games wit h five or more players. This note extends Young's result. No core allocatio n method can be coalitionally monotonic on cooperative games with four of m ore players, and there is an infinite class of core allocation methods that are coalitionally monotonic on three-player cooperative games.