Show by example that the game qx x is not necessarily a

Question

Let (N; v) be a simple strong game, and let x ∈ X(N; v) be an imputation. Recall that q(x) := minS∈Wm x(S). Answer the following questions:

(a) Show by example that the game [q(x); x] is not necessarily a simple strong game. Which property in the definition of a simple strong game may not hold?

(b) Denote by Wmx the set of minimal winning coalitions in the game [q(x); x].Prove that Wm ⊆ W^m_x.

(c) Give an example showing that the inclusion Wm ⊆W^m_x can be strict.