Consider the following matrix game Find u1sigma1 M for sigma

Consider the following matrix game. Find u_1(sigma_1, M) for sigma_1 = (1/10, 1/5, 7/10). Find u_2 (sigma_1, R) for sigma_1 = (1/3, 0, 2/3). Find u_1(sigma_2, sigma_2) for sigma_1 = (1/3, 1/2, 1/6) and sigma_2 = (1/8, 3/8, 1/2). Find u_2(sigma_1), sigma_2 for sigma_1 = (1/3, 1/2, 1/6) and sigma_2 = (1/8, 3/8, 1/2).

Solution

(a) If player 2 chooses M, player 1 gets 0 with probability 1/10, it gets 1 with probability 1/5,and gets 2 with probability 7/10.

u1=0(1/10)+1(1/5)+2(7/10)=16/10

(b) If player 2 chooses R, player 2 gets 0 with probability 1/3, it gets 0 with probability 0 and gets 1 with probability 2/3.

u2=0(1/3)+0(0)+1(2/3)=2/3

(c) u1=8(1/3)(1/8)+4(1/3)(1/2)+3(1/3)(1/8)+1(1/2)(3/8)+5(1/3)(1/8)+2(1/2)(3/8)+8(1/6)(1/2)

u1=123/48

(d) u2=1(1/3)(1/8)+3(1/8)(1/2)+2(1/3)(3/8)+2(1/2)(3/8)+3(1/6)(3/8)+1(1/6)(1/2)

u2= 27/24