(a) Is the three-player game (N; v) in which v is given by monotonic? Justify your answer.
v(1) = 3,
v(2) = 13,
v(3) = 4,
v(1,2) = 12,
v(1,3) = 15,
v(2,3) = 1,
v(1,2,3) = 10,
(b) Find a monotonic game that is strategically equivalent to (N; v).
(c) Prove that every game is strategically equivalent to a monotonic game. It follows that the property of monotonicity is not invariant under strategic equivalence.