1. Solve the following game graphically -5 5 -1 8 -4 6 A

2. Solution. -5 5 -1 8 -4 6 1 2

3. If B select strategy Expected pay off of A
Since, Maximax ≠ Maximin Thus, players will use the mixed strategy Since, we do not have saddle point Let p1 the probability of Mr A selecting strategy I & Hence (1- p1) be the probability of Mr A selecting stratety2
If B select strategy
Expected pay off of A 1 2 3 4 5
-5 (p1)+8 (1-p1)= -13p1 +8
5 (p1) -4 (1-p1)= 9p1-4
0 (p1) +-1(1-p1)= p1-1
-1 (p1) + 6 (1-p1)= -7p1+6
8 (p1) +-5 (1-p1)= 13p1-5

4. we plot these values on the graph given below:11 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 11 10 9 8 7 6 5 4 3 2 1 -1 -4 -5 B5 B1
13p1-5
9p1-4
-7p1+6 B4
B3 p1-1 Q R
B11
-13p1+8
Maximin B1 P
LOWER ENVELOP

5. Since R is the maximin point and here B, B3 interesect
Since R is the maximin point and here B, B3 interesect. These strategies will be selected & the resultant matrix is the produced below.
Odds 5
Odds -5 8 -1

6. V = a1 (b1-b2)+ b1 (a1-a2) ______________________= (b1-b2)+ (a1-a2)
(-5×9)+(8×5) =-5/14 9+5

7. Probability of selecting strategies No.
Probablility of selecting strategies No 1 2
9/14
5/14 3 4 5
1/14
13/14