If n v and n w are superadditive games and if 0 le lambda

Question

Prove that the convex combination of superadditive games is also superadditive.

In other words, if (N; v) and (N; w) are superadditive games, and if 0 ≤ λ ≤ 1, then the game (N , λv + (1 - λ)w) defined by

(λv + (1 - λ)ω) (S) := λv(S) + (1 - λ) ω(s)

is also superadditive.