Consider a two-player non-zero-sum game on the unit square in which Player I's strategy set is X = [0, 1], Player II's strategy set is Y = [0, 1], and the payoff functions for the players are given below.
Find the maxmin value and the maxmin strategy (or strategies) of the players. Does this game have an equilibrium? If so, find it.
(a) u(x,y) = 1 + 4x + y - 5xy.
(b) u(x,y) = 4 + 2y - 4xy.