game theory: an introduction
DESCRIPTION
Introduction to Game Theory Type of Games Dominant Games Nash Equilibrium Multiple EquilibriumTRANSCRIPT
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Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 1
DATA MINING AND MACHINE LEARNINGIN A NUTSHELL
GAME THEORY, AN INTRODUCTION
Mohammad-Ali Abbasihttp://www.public.asu.edu/~mabbasi2/
SCHOOL OF COMPUTING, INFORMATICS, AND DECISION SYSTEMS ENGINEERINGARIZONA STATE UNIVERSITY
http://dmml.asu.edu/
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Agenda
• History
• Introduction to Game Theory
• Type of Games– Dominant Games– Nash Equilibrium– Multiple Equilibrium
• Game Time
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Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 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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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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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.
6
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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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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• Review a Game• Characteristics• Rules• Assumptions
Introduction to Game Theory
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Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 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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Prisoners dilemma
• Introduction
TomNot
ConfessConfess
Jack
Not Confess -1, -1 -8, 0
Confess 0, -8 -4, -4
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Jack’s Decision Tree
If Tom Does Not ConfessIf Tom Confesses
Jack
4 Years in Prison
8 Years in Prison
Free1 Years in
Prison
Jack
Not ConfessConfess Confess Not Confess
BestStrategy Best
Strategy
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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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• Dominant Games• Nash Equilibrium• Multiple Equilibrium
Types of Games
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Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 18
Prisoner’s Dilemma
If Tom Does Not ConfessIf Tom Confesses
Jack
4 Years in Prison
8 Years in Prison
Free1 Years in
Prison
Jack
Not ConfessConfess Confess Not Confess
BestStrategy Best
Strategy
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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 BLow Price Upscale
Firm A
Low Price
.48, .12 .6, .4
Upscale .4, .6 .32, .08
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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 2A B C
Firm 1
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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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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• Coordination Game• The Hawk-Dove Game
Multiple Equilibriums
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Coordination Game
Your PartnerPower Point Keynote
You
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 PartnerPower Point Keynote
You
Power Point
1, 1 0, 0
Keynote 0, 0 2, 2
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Battle of the Sexes
WifeRomantic Action
Husband
Romantic 1, 2 0, 0
Action 0, 0 2, 1
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Stag Hunt Game
Hunter 2Stag Hare
Hunter 1
Stag 4, 4 0, 3
Hare 3, 0 3, 3
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Hawk- Dove game
Animal 2Dove Hawk
Animal 1
Dove 3, 3 1, 5
Hawk 5, 1 0, 0
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Mixed Strategies- Matching Pennies
Zero-sum Game Player 2
Head Tail
Player 1
Head -1, +1 +1, -1
Tail +1, -1 -1, +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/