In a two-player zero-sum game on the unit square where Player I's strategy set is X = [0, 1] and Player II's strategy set is Y = [0, 1],
check whether or not the game associated with each of the following payoff functions has a value, and if so, find the value and optimal strategies for the two players:
(a) u(x,y) = 1 + 4x + y - 5xy.
(b) u(x,y) = 4 + 2y - 4xy.