Prove that a three-player 0-normalized game whose core is nonempty, and satisfying v(S) ≥ 0…

Prove that a three-player 0-normalized game whose core is nonempty, and satisfying v(S) ≥ 0 for every coalition S, is monotonic. Is this true also for games with more than three players? Justify your answer. Does it hold true without the condition that v(S) ≥ 0 for every coalition? Justify your answer.