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
Data Mining and Machine Learning Lab
http://dmml.asu.edu/
Data Mining and Machine Learning- in a nutshell
An Introduction to Game Theory
1
Agenda
• History
• Introduction to Game Theory
• Type of Games
– Dominant Games
– Nash Equilibrium
– Multiple Equilibrium
• Game Time
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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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An Introduction to Game Theory
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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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An Introduction to Game Theory
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4
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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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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Decision theory vs. Game theory
• Decision Theory
– You are self-interested and selfish
• Game Theory
– So is everyone else
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7
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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An Introduction to Game Theory
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8
Introduction to Game Theory
•
•
•
•
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Review a Game
Characteristics
Rules
Assumptions
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An Introduction to Game Theory
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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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Prisoners dilemma
• Introduction
Tom
Not
Confess
Confess
Not Confess
-1, -1
-8, 0
Confess
0, -8
-4, -4
Jack
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Jack’s Decision Tree
If Tom Confesses
If Tom Does Not Confess
Jack
Confess
4 Years in
Prison
Jack
Not Confess
8 Years in
Prison
Best
Strategy
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Confess
Not Confess
1 Years in
Prison
Free
Best
Strategy
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An Introduction to Game Theory
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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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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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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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Types of Games
• Dominant Games
• Nash Equilibrium
• Multiple Equilibrium
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Prisoner’s Dilemma
If Tom Confesses
If Tom Does Not Confess
Jack
Confess
4 Years in
Prison
Jack
Not Confess
8 Years in
Prison
Best
Strategy
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Confess
Not Confess
1 Years in
Prison
Free
Best
Strategy
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An Introduction to Game Theory
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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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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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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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Marketing Strategy
• Dominant Games
Firm B
Low Price
Upscale
Firm A
Low
.48, .12
Price
Upscale
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.4, .6
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.6, .4
.32, .08
An Introduction to Game Theory
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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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Marketing Strategy
• Nash Equilibrium
Firm 1
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A
Firm 2
B
C
A
4, 4
0, 2
0, 2
B
0, 0
1, 1
0, 2
C
0, 0
0, 2
1, 1
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An Introduction to Game Theory
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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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Multiple Equilibriums
• Coordination Game
• The Hawk-Dove Game
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Coordination Game
Your Partner
Power Point Keynote
You
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Power
Point
1, 1
0, 0
Keynote
0, 0
1, 1
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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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Unbalanced Coordination Game
Your Partner
Power Point Keynote
You
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Power
Point
1, 1
0, 0
Keynote
0, 0
2, 2
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Battle of the Sexes
Wife
Romantic
Action
Husba
nd
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Romantic
1, 2
0, 0
Action
0, 0
2, 1
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An Introduction to Game Theory
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Stag Hunt Game
Hunter 2
Stag
Hare
Stag
4, 4
0, 3
Hare
3, 0
3, 3
Hunter 1
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Hawk- Dove game
Animal 2
Dove
Hawk
Dove
3, 3
1, 5
Hawk
5, 1
0, 0
Animal 1
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Mixed Strategies- Matching Pennies
Zero-sum
Game
Player 2
Head
Tail
Head
-1, +1
+1, -1
Tail
+1, -1
-1, +1
Player 1
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Be ready for a Game!
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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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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/
Arizona State University
Data Mining and Machine Learning Lab
Data Mining and Machine Learning- in a nutshell
An Introduction to Game Theory
36