Player i in a coalitional game (N; v) is a dummy player if
v(S ∪ {i}) = v(S) + v(i), ∀S ⊆ N|{i}.
Prove that if player i is a dummy player in a game (N; v) then under both the nucleolus and the prenucleolus, player i's payoff is v(i), that is, Ni(N; v) = v(i) and PN i(N; v) = v(i).