Games with restricted cooperation are cooperative N-person games with sidepayments, where the collection of feasible coalitions need not comprise all subsets of players and thus is restricted. The paper studies balanced and completely balanced games in this context and derives the corresponding core theorems from a sandwich theorem for set functions within the setting of linear programming. In particular, it discusses general convex games, which Edmonds and Giles have shown to be of particular importance also in combinatorial optimization.