Prove that the core is a convex set. That is, show that for any two imputations x, y in the core…

Prove that the core is a convex set. That is, show that for any two imputations x, y in the core of a coalitional game (N; v), and for all α ∈ [0, 1], the imputation αx + (1 − α)y is also in the core of the game (N; v).