The document provides an introduction to game theory, covering its history, key concepts, and applications. It discusses how game theory analyzes strategic decision-making between interdependent actors. The document outlines different types of games including dominant games, Nash equilibriums, and multiple equilibrium games. It also presents examples like the prisoner's dilemma game to illustrate game theory concepts and strategies.

1. DATA MINING AND MACHINE LEARNING
IN A NUTSHELL
GAME THEORY,
AN INTRODUCTION
Mohammad-Ali Abbasi
http://www.public.asu.edu/~mabbasi2/
SCHOOL OF COMPUTING, INFORMATICS, AND DECISION SYSTEMS ENGINEERING
ARIZONA STATE UNIVERSITY
Arizona State University
http://dmml.asu.edu/
Data Mining and Machine Learning Lab
Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 1

2. Agenda
• History
• Introduction to Game Theory
• Type of Games
– Dominant Games
– Nash Equilibrium
– Multiple Equilibrium
• Game Time
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3. History
• Interdisciplinary (Economic and Mathematic)
approach to the study of human behavior
• Founded in the 1920s by John von Neumann
• 1994 Nobel prize in Economics awarded to
three researchers
• “Games” are a metaphor for wide range of
human interactions
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4. What is a Game
• Game theory is concerned with situations in
which decision-makers interact with one
another,
• and in which the happiness of each participant
with the outcome depends not just on his or
her own decisions but on the decisions made
by everyone.
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5. A Game!
• Ten of you go to a restaurant
• If each of you pays for your own meal…
– This is a decision problem
• If you all agree to split the bill...
– Now, this is a game
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6. Restaurant Decision-Making
• Bill splitting policy changes incentives.
May I recommend that with the Bleu
Cheese for ten dollars more?
Sure!
It is only
a dollar more
for me!
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7. Decision theory vs. Game theory
• Decision Theory
– You are self-interested and selfish
• Game Theory
– So is everyone else
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8. Applications
• Market:
– pricing of a new product when other firms have similar new products
– deciding how to bid in an auction
• Networking:
– choosing a route on the Internet or through a transportation networks
• Politic:
– Deciding whether to adopt an aggressive or a passive stance in
international relations
• Sport:
– choosing how to target a soccer penalty kick and choosing how to
defend against
– Choosing whether to use performance-enhancing drugs in a
professional sport
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9. Introduction to Game Theory
• Review a Game
• Characteristics
• Rules
• Assumptions
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10. The Prisoner’s Dilemma
• Two burglars, Jack and Tom, are captured and
separated by the police
• Each has to choose whether or not to confess and
implicate the other
• If neither confesses, they both serve one year for
carrying a concealed weapon
• If each confesses and implicates the other, they
both get 4 years
• If one confesses and the other does not, the
confessor goes free, and the other gets 8 years
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11. Prisoners dilemma
• Introduction
Tom
Not Confess
Confess
Not Confess -1, -1 -8, 0
Jack
Confess 0, -8 -4, -4
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12. Jack’s Decision Tree
If Tom Confesses If Tom Does Not Confess
Jack Jack
Confess Not Confess Confess Not Confess
4 Years in 8 Years in 1 Years in
Free
Prison Prison Prison
Best
Best
Strategy
Strategy
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13. Basic elements of a Game
• Players
– Everyone who has an effect on your earnings
• Strategies
– Actions available to each player
– Define a plan of action for every contingency
• Payoffs
– Numbers associated with each outcome
– Reflect the interests of the players
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14. Assumptions in the Game Theory
• Player
– We assume that each player knows everything about the
structure of the game
– Player don’t know about another’s decision
– Each player knows the rules of the game
– Players are rational and expert
• Strategy
– Each player has two or more well-specified choices
– Each player chooses a strategy to maximize his own payoff
– Every possible combination of strategies available to the players
leads to a well-defined end-state (win, loss, draw) that
terminates the game
• Payoff
– everything that a player cares about is summarized in the
player's payoffs
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15. Basic Games
• games with only two players
– We can apply it on any number of players
• simple, one-shot games
– Simultaneously, Independent and only once
– Not dynamic
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16. Types of Games
• Dominant Games
• Nash Equilibrium
• Multiple Equilibrium
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17. Prisoner’s Dilemma
If Tom Confesses If Tom Does Not Confess
Jack Jack
Confess Not Confess Confess Not Confess
4 Years in 8 Years in 1 Years in
Free
Prison Prison Prison
Best
Best
Strategy
Strategy
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18. Dominant strategy
• A players has a dominant strategy if that
player's best strategy does not depend on
what other players do.
P1(S,T) >= P1 (S’, T)
• Strict Dominant strategy
P1(S,T) > P1 (S’, T)
• Games with dominant strategies are easy to
play
– No need for “what if …” thinking
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19. Prisoner's Dilemma
• Strategies must be undertaken without the
full knowledge of what other players will do.
• Players adopt dominant strategies,
• BUT they don't necessarily lead to the best
outcome.
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20. If only one player has Strictly dominant Strategy
• Players: Firm A and Firm B
– Produce a new product
• Options: Low Price and Upscale
• 60% of people would prefer low price and 40% high
price
• Firm A is dominant and can gets 80% of market
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21. Marketing Strategy
• Dominant Games
Firm B
Low Price Upscale
Low
.48, .12 .6, .4
Price
Firm A
Upscale .4, .6 .32, .08
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22. A three client Game
• Two Firms: Firm 1 and Firm 2
• Three Clients: Client A, B and C
• Conditions:
– If two firms apply for same client can get half of its
business
– Firm 1 is too small to attract a business -> payoff =
0
– If firm 2 approaches to B or C on its own, it will
take all their business (their business is worth 2)
– A is larger client and its business is worth 8. they
can work with it if both of them target it.
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23. Marketing Strategy
• Nash Equilibrium
Firm 2
A B C
A 4, 4 0, 2 0, 2
Firm 1 B 0, 0 1, 1 0, 2
C 0, 0 0, 2 1, 1
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24. Nash Equilibrium
• A Nash equilibrium is a situation in which
none of them have dominant Strategy and
each player makes his or her best response
– (S, T) is Nash equilibrium if S is the best strategy to
T and T is the best strategy to S
• John Nash shared the 1994 Nobel prize in
Economic for developing this idea!
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25. Multiple Equilibriums
• Coordination Game
• The Hawk-Dove Game
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26. Coordination Game
Your Partner
Power Point Keynote
Power
1, 1 0, 0
Point
You
Keynote 0, 0 1, 1
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27. Other samples of Coordination Game
• Using Metric units of measurement of English
Units
• Two people trying to find each other in a
crowded mall with two entrance
• …
• These games has more than one Nash
Equilibrium
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28. Unbalanced Coordination Game
Your Partner
Power Point Keynote
Power
1, 1 0, 0
Point
You
Keynote 0, 0 2, 2
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29. Battle of the Sexes
Wife
Romantic Action
Romantic 1, 2 0, 0
Husba
nd
Action 0, 0 2, 1
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30. Stag Hunt Game
Hunter 2
Stag Hare
Stag 4, 4 0, 3
Hunter 1
Hare 3, 0 3, 3
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31. Hawk- Dove game
Animal 2
Dove Hawk
Dove 3, 3 1, 5
Animal 1
Hawk 5, 1 0, 0
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32. Mixed Strategies- Matching Pennies
Zero-sum
Game Player 2
Head Tail
Head -1, +1 +1, -1
Player 1
Tail +1, -1 -1, +1
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33. Be ready for a Game!
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34. play a real game!
• Select a random number between 0 and 100
• The winner is the one how, his number is closest
to 0.75 of the average.
– If average is AVG, closest number to AVG * 0.75 is
winner
• Score distribution:
– 1st : 100
– 2nd : 50
– Others: 0
• Talk about your selection
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35. Mohammad-Ali Abbasi (Ali),
Ali, is a Ph.D student at Data Mining
and Machine Learning Lab, Arizona
State University.
His research interests include Data
Mining, Machine Learning, Social
Computing, and Social Media Behavior
Analysis.
http://www.public.asu.edu/~mabbasi2/
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