Note Core and monotonic allocation methods

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