Page 205 - Probability Demystified

194 CHAPTER 11 Game Theory

General A’s expected payoff if he attacks and General B defends by land is
$25p þ $90(1 p) and if General B defends by sea is $75p $50(1 p).
Equating the two and solving for p, we get

25p þ 90ð1 pÞ¼ 75p 50ð1 pÞ
25p þ 90 90p ¼ 75p 50 þ 50p

115p þ 90 ¼ 125p 50

115p 125p þ 90 ¼ 125p 125p 50
240p þ 90 ¼ 50

240p þ 90 90 ¼ 50 90
240p ¼ 140

240p 140
¼
240 240
7
p ¼
12
Hence General A should attack by land 7 of the time and by sea 5 of the
12 12
time. The value of the game is

25p þ 90ð1 pÞ

7 5
¼ 25 þ 90
12 12

¼ $22:92

Now let us figure out General B’s strategy.
General B should defend by land with a probability of s and by sea with a
probability of 1 s. Hence,