Deep Thought
I can picture in my mind a
world without war, a world
without hate. And I can
picture us attacking that
world, because they’d never
expect it. --- by Jack
Handey.
BA 592 Lesson I.1 Introducing Games
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Welcome to BA 592
Game Theory
Acknowledgements
The course content is adapted from the textbook
Games of Strategy
third edition, published by W.W. Norton & Company © 2009.
BA 592 Lesson I.1 Introducing Games
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Welcome to BA 592
Game Theory
Getting acquainted
What is Game Theory?
Game Theory finds optimal decisions when payoffs to a player
depend on the decisions of other players as well as the player
himself. Game Theory is also known as multi-person decision
theory.
The course focuses on formulating and solving games to find
optimal business strategies and economic policies. Applications
include bargaining, lending, dividing pirate gold, … .
BA 592 Lesson I.1 Introducing Games
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Welcome to BA 445
Managerial Economics
Getting started
Read and bookmark the online course syllabus.
http://faculty.pepperdine.edu/jburke2/Game/index.htm
It serves as a contract specifying our obligations to each other.
(You may need to use Internet Explorer.) In particular, note:
 Introduction to Microeconomics, Statistics, and Calculus are
prerequisites, so review as needed.
 Before each class meeting, download and read the PowerPoint
lesson, as presented under the “Schedule” link.
BA 592 Lesson I.1 Introducing Games
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Lesson overview
Chapter 1 Basic Ideas and Examples
Lesson I.1 Introducing Games
What is a Game?
Example 1: Prisoners’ Dilemma
Example 2: Penalty Kick
Example 3: Predicting Current Strategies
Example 4: Predicting Future Strategies
BA 592 Lesson I.1 Introducing Games
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What is a Game?
What is a Game?
• There are many types of games --- board games (Monopoly, …),
card games (poker, …), video games (Warcraft,…), and field games
(football,…).
• We focus on games where:
n
n
n
n
There are 2 or more players.
There is some choice of action where strategy matters.
The game has outcomes; often, someone wins, someone loses.
Outcomes depend on the strategies chosen by all players: there is
strategic interaction.
• What does that rule out?
n
n
Games of pure chance, like lotteries and slot machines, since strategies
don't matter.
Games without strategic interaction between players, like Solitaire;
there are strategies, but no interaction.
BA 592 Lesson I.1 Introducing Games
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What is a Game?
Why Study Games?
• Games aim to be useful models of strategic interactions among
economic agents.
• Many business and economic decisions involve strategic
interaction.
n Behavior in imperfectly competitive markets, like CocaCola versus Pepsi.
n Behavior in economic negotiations, like wages.
n Behavior in auctions, like investment banks bidding on
U.S. Treasury bills.
• Game theory is not limited to Business and Economics.
n The Cuban Missile Crisis was a game of chicken.
BA 592 Lesson I.1 Introducing Games
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What is a Game?
Game Theory is useful for explanation.
• Economic historians ask: Why did that happen?
• Why did two agents hurt each other, rather that cooperate?
n Why did makers of personal computers engage in cutthroat
competition that resulted in bankruptcies?
n Why did the U.S. and Soviet Union spend so much money
on the arms race?
• Why did other agents cooperate, and avoid competition?
n Why is the OPEC cartel sometimes effective at raising the
price of oil?
BA 592 Lesson I.1 Introducing Games
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What is a Game?
Game Theory is useful for prediction.
• Economists ask: What will happen after a change in public
policy?
• Will two agents continue to hurt each other?
• Will two agents continue to cooperate?
BA 592 Lesson I.1 Introducing Games
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What is a Game?
Game Theory is useful for advice or prescription.
• Managers ask: Which strategies are optimal?
• Which are likely to lead to disaster?
BA 592 Lesson I.1 Introducing Games
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Example 1: Prisoners’ dilemma
Prisoners’ dilemma
1. You are in a course graded on a curve: 20% A’s, … .
2. The other students agree to not work too hard.
3. You must decide whether to enter into that agreement.
• Can you trust other students to live up the agreement?
• What factors would affect whether students can be trusted?
• We begin studying repeated games in Part II of the course.
• Can a prisoner trust his partner in crime to not confess?
• Can you trust your roommate with $10 left on a table? $1000?
• Can you trust a fellow Greyhound bus passenger with $1?
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Example 2: Penalty Kick
Strategic Uncertainty is not knowing the strategies or actions of
other players. You always want to reduce your own strategic
uncertainty. Sometimes, you want to reduce the strategic
uncertainty of your opponents, like telling them of your
marketing a new drug so they will give up marketing a substitute
drug. Other times, you want to increase your opponents’ strategic
uncertainty.
BA 592 Lesson I.1 Introducing Games
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Example 2: Penalty Kick
Stopping a soccer penalty kick is quite a feat
By Gary Mihoces, USA TODAY
• "When you consider that a ball can be struck anywhere from 60-80 miles per
hour, there's not a whole lot of time for the goalkeeper to react," says Bob
Gustavson, professor of health science and men's soccer coach at John
Brown University in Siloam Springs, Ark.
• Gustavson says skillful goalies use cues from the kicker. They look at where
the kicker's plant foot is pointing and the posture during the kick. Some even
study tapes of opponents. But most of all they take a guess — jump left or
right after the kicker has committed himself.
• Following an unpredictable strategy means randomly selecting one or
more actions, like a goalie jumping left or jumping right.
• The strategy can be right, even when the action fails!
• We begin studying unpredictable strategies in Part II of the course.
BA 592 Lesson I.1 Introducing Games
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Example 3: Predicting Current Strategies
Outcomes of a game depend on the strategies chosen by all
players, so you should predict your opponents’ strategies before
you choose your own. When your opponents’ strategies are
chosen at the same time as yours, you must predict what your
opponent will do now, recognizing that your opponent is doing
the same.
BA 592 Lesson I.1 Introducing Games
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Example 3: Predicting Current Strategies
Guess 2/3 of the average
1. No talking or other communication between players.
2. Players secretly write a real number between 0 and 100.
3. The winner is the one closest to 2/3 of the average.
4. The winner in this class gets $1.00. If there is a tie, the
$1.00 will be evenly divided.
Why did you choose your particular number?
Will you play differently next time?
BA 592 Lesson I.1 Introducing Games
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Example 4: Predicting Future Strategies
Opponents’ strategies might also be chosen after yours, so you
must predict what your opponent will do in the future,
recognizing that your opponent can react to your strategy.
BA 592 Lesson I.1 Introducing Games
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Example 4: Predicting Future Strategies
Five Pirates find 100 gold coins. They must decide how to distribute them.
The Pirates have a strict order of seniority: Pirate A is senior to B, who is
senior to C, who is senior to D, who is senior to E.
The Pirate world's rules of distribution are thus: the most senior pirate should
propose a distribution of coins. The pirates, including the proposer, then vote
on whether to accept this distribution. If the proposed distribution is approved
by a majority or a tie vote, it happens. If not, the proposer is thrown overboard
from the pirate ship and dies, and the next most senior pirate makes a new
proposal to begin the system again.
Pirates base their decisions on three factors. Firstly, each pirate wants to
survive. Secondly, each pirate wants to maximize the amount of gold coins he
receives. Thirdly, each pirate prefer to throw another overboard, if doing so
does not decrease his own gold coins.
Can Pirate A survive? If so, what distribution of coins should he propose?
BA 592 Lesson I.1 Introducing Games
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Example 4: Predicting Future Strategies
Pirate A needs to predict which distributions are acceptable to the
other pirates. That, in turn, depends on which distributions the
other pirates can expect if they throw Pirate A overboard. To
predict those distributions, start from the end of the possible ends
of the game and work backward:
• If 2 pirates remain (D and E), D proposes 100 for himself and
0 for E. He has the casting vote, and so this is the allocation.
• If 3 pirates remain (C, D and E), C knows that D will offer E 0
in the next round; therefore, C has to offer E 1 coin in this
round to make E vote with him and get his distribution through
(he cannot offer less because E prefers to throw C overboard if
he were offered 0 gold). Therefore, when only three pirates are
left, the distribution is C:99, D:0, E:1.
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Example 4: Predicting Future Strategies
• If 4 pirates remain (B, C, D and E), B knows the distribution
will be C:99, D:0, E:1 if he were thrown overboard. To avoid
being thrown overboard, B can simply offer 1 to D (he cannot
offer less because D prefers to throw B overboard if he were
offered 0 gold). Because he has the casting vote, the support
only by D is sufficient. Thus the distribution is B:99, C:0, D:1,
E:0.
• When A proposes a distribution to all 5 pirates (A, B, C, D and
E), A knows the distribution will be B:99, C:0, D:1, E:0 if he
were thrown overboard. To avoid being thrown overboard, A
can simply offer 1 to C and E (he cannot offer less because
either C or E prefer to throw A overboard if he were offered 0
gold). Because he has the casting vote, the support only by C
and E is sufficient. Thus A should propose A:98, B:0, C:1, D:0,
E:1.
BA 592 Lesson I.1 Introducing Games
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BA 592
Game Theory
End of Lesson I.1
BA 592 Lesson I.1 Introducing Games
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