1. Consider an agent who takes an action after receiving some in- formation. A decision problem is a tuple (S, II, C, u, p), where S is the state space, II is the partition, C is the set of actions, u Sx C R is the utility function and p is the prior over S. Show that if partition II is finer than partition II then decision problem A = (S, II, C, u, p) is more valuable than decision problem B = (S, I1, C, u, p).