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/

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 2

Agenda

• History

• Introduction to Game Theory

• Type of Games– Dominant Games– Nash Equilibrium– Multiple Equilibrium

• Game Time

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 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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Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 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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Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 6

Restaurant Decision-Making

• Bill splitting policy changes incentives.

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May I recommend that with the Bleu Cheese for ten dollars more?

Sure!

It is only a

dollar more for me!

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 7

Decision theory vs. Game theory

• Decision Theory– You are self-interested and selfish

• Game Theory– So is everyone else

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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 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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Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 9

• Review a Game• Characteristics• Rules• Assumptions

Introduction to Game Theory

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 11

Prisoners dilemma

• Introduction

TomNot

ConfessConfess

Jack

Not Confess -1, -1 -8, 0

Confess 0, -8 -4, -4

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 12

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 16

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 17

• Dominant Games• Nash Equilibrium• Multiple Equilibrium

Types of Games

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 19

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 20

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.

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 21

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 22

Marketing Strategy

• Dominant Games

Firm BLow Price Upscale

Firm A

Low Price

.48, .12 .6, .4

Upscale .4, .6 .32, .08

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 23

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.

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 24

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 25

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!

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 26

• Coordination Game• The Hawk-Dove Game

Multiple Equilibriums

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 27

Coordination Game

Your PartnerPower Point Keynote

You

Power Point

1, 1 0, 0

Keynote 0, 0 1, 1

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 28

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 29

Unbalanced Coordination Game

Your PartnerPower Point Keynote

You

Power Point

1, 1 0, 0

Keynote 0, 0 2, 2

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 30

Battle of the Sexes

WifeRomantic Action

Husband

Romantic 1, 2 0, 0

Action 0, 0 2, 1

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 31

Stag Hunt Game

Hunter 2Stag Hare

Hunter 1

Stag 4, 4 0, 3

Hare 3, 0 3, 3

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 32

Hawk- Dove game

Animal 2Dove Hawk

Animal 1

Dove 3, 3 1, 5

Hawk 5, 1 0, 0

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 33

Mixed Strategies- Matching Pennies

Zero-sum Game Player 2

Head Tail

Player 1

Head -1, +1 +1, -1

Tail +1, -1 -1, +1

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 34

Be ready for a Game!

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 35

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

Data Mining and Machine Learning- in a nutshellArizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 36

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/