Suppose we have a zero sum game and mixed densities X0 for player I and Y0 for player II.

(a) Suppose there are constants c and b so that u(X0, y) = c for all pure strategies y for player II and u(x , Y0) = b, for all pure strategies x for player II. Show that (X0, Y0) is a saddle point in mixed strategies for the game and we must have b = c.
(b) Suppose there is a constant c so that u(X0, y) ≥ c, for all pure x , and u(x , Y0) ≤ c, for all pure y. Show that (X0, Y0) is a saddle point in mixed strategies.