Two persons agree to play the following game: The first writes either 1 or 4 on a slip of paper, and at the same time the second writes either 0 or 3 on another slip of paper. If the sum of the two numbers is odd, the first wins this amount in dollars; otherwise, the second wins $ 2. 

(a) Construct the payoff matrix in which the payoffs are the first person’s losses.

(b) What randomized decision procedure should the first person use so as to minimize her maximum expected loss? 

(c) What randomized decision procedure should the second person use so as to maximize his minimum expected gain?