Page 216 - Probability Demystified

CHAPTER 11 Game Theory 205

0:8s þ 0:4 0:4 ¼ 0:2 0:4

0:8s ¼ 0:2

0:8s 0:2
¼
0:8 0:8
1
s ¼
4
Hence, player B must defend against a long shot 1 4 of the time, and
against a lay-up shot 3 of the time.
4

Summary

Game theory uses mathematics to analyze games. These games can range
from simple board games to warfare. A game can be considered a contest
between two players and consists of rules on how to play the game and how
to determine the winner. In this chapter, only two-player, zero sum games
were explained. A payoff table is used to determine how much a person wins
or loses. Payoff tables can also consist of probabilities.
A strategy is a rule that determines a player’s move or moves in order to
win the game or maximize the player’s payoff. An optimal strategy is the
strategy that a player uses that will guarantee him or her an average payoff of
a certain amount no matter what the other player does. An optimal strategy
for a player could also be one that will prevent the other player from
obtaining an average payoff greater that a certain amount. This amount is
called the value of the game. If the value of the game is zero, then the game
is fair.

CHAPTER QUIZ

1. The person who developed the concepts of game theory was
a. Garry Kasparov
b. Leonhard Euler
c. John Von Neumann
d. Blase ´ Pascal