Subadditive and homogeneous of degree one games are totally balanced

A cooperative game with transferable utility is said to be homogeneous of degree one if for any integer m, the value of cloning m times all players at any given coalition, leads to m times the value of the original coalition. We show that this property coupled with subadditivity, guarantees the nonemptyness of the core of the game and of all its subgames, namely, the game is totally balanced. Examples for games stemming from the areas of retailing and of facility location are given.