Page 214 - Probability Demystified

CHAPTER 11 Game Theory 203

4. The payoff table is

Inspector:

Vendor: Main St. Railroad Ave.
Main St. $50 $100

Railroad Ave. $75 $50

Let p be the probability that the vendor selects Main St. and 1 p be
the probability that the vendor selects Railroad Ave. Then,
50p þ 75ð1 pÞ¼ 100p 50ð1 pÞ

50p þ 75 75p ¼ 100p 50 þ 50p

125p þ 75 ¼ 150p 50

125p 150p þ 75 ¼ 150p 150p 50
275p þ 75 ¼ 50

275p þ 75 75 ¼ 50 75

275p ¼ 125

275p 125
¼
275 275
125 5
p ¼ ¼
275 11

The value of the game when p ¼ 5 is
11

5 5
50p þ 75ð1 pÞ¼ 50 þ 75 1
11 11

5 6
¼ 50 þ 75
11 11
2
¼ 18 18:18
11