Consider the three-player game G with the payoffs given in Table 1. (Player 1 may choose Table 1: Payoffs of G U D L R L R N (2, 1, 2) (2, 1, 2) (0,0,0) (0,0,0) E (1,0,1) (1, 0, 1) (2,1,2) :) ( W (2, 1, 2) (2,1,2) (2, 1, 2) (1, 0, 1) (0, 0, 0) (2, 1, 2) (0, 0, 0) S (1,0,1) (2,1,2) each of the rows N, E, W, S, Player 2 each of the columns L, R, and Player 3 each of the two matrices U, D.) Let (p, q, r, s), (y, 1-y), and (z, 1-2) be typical mixed strategies of Player 1, Player 2, and Player 3, respectively. Show that there is a unique pair ((y, 1-y), (z, 1-z)) of mixed strategies of 2 and 3 such that Player 1 is indifferent between all rows. (Hint: Player 2 must guarantee that 1 is indifferent between W and S, and 3 must guarantee that 1 is indifferent between N and E).