Assignment:
Let (N; v) be a coalitional game satisfying the following property: there is an imputation x ∈ X(N; v) such that all the excesses at x are nonnegative.
(a) Prove that x is the only imputation in the game, and in particular it is the nucleolus.
(b) Is x necessarily also the prenucleolus? Either prove this statement, or provide a counterexample.
Provide complete and step by step solution for the question and show calculations and use formulas.