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Sticky Content and the Structure of the Web Scott Duke Kominers Harvard University Workshop on the Economics of Networks, Systems, and Computation July 7, 2009 Scott Duke Kominers (Harvard) NetEcon09 July 7, 2009 1 / 17 Introduction

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SLIDE 1

Sticky Content and the Structure of the Web

Scott Duke Kominers

Harvard University

Workshop on the Economics of Networks, Systems, and Computation July 7, 2009

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 1 / 17

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SLIDE 2

Introduction

What is “sticky content”?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 3

Introduction

What is “sticky content”?

Sticky content is....

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 4

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 5

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 6

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 7

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 8

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates horoscopes

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 9

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates horoscopes webmail

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 10

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates horoscopes webmail

  • nline games

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 11

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates horoscopes webmail

  • nline games

Observation

Sticky content is prevalent on the internet.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

slide-12
SLIDE 12

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates horoscopes webmail

  • nline games

Observation

Sticky content is prevalent on the internet.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 13

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates horoscopes webmail

  • nline games

Observation

Sticky content is prevalent on commercial sites/portals.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 14

Introduction

What is “sticky content”?

Sticky content is website content which induces return traffic and holds user attention. news/weather updates horoscopes webmail

  • nline games

Observation

Sticky content is prevalent on commercial sites/portals.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 2 / 17

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SLIDE 15

Introduction

Why study sticky content?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 16

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 17

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover...

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 18

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received little attention

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 19

Introduction

Why study sticky content?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 20

Introduction

Why study sticky content?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 21

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received little attention

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 22

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received very little attention

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 23

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received very little attention

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 24

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received very little attention Sticky content may be universally beneficial

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 25

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received very little attention Sticky content may be universally beneficial

for content providers

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 26

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received very little attention Sticky content may be universally beneficial

for content providers (marketers believe)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 27

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received very little attention Sticky content may be universally beneficial

for content providers (marketers believe) for consumers

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 28

Introduction

Why study sticky content?

Observation

Sticky content is prevalent on commercial sites/portals. Moreover... Sticky content has received very little attention Sticky content may be universally beneficial

for content providers (marketers believe) for consumers (conjectural)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 3 / 17

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SLIDE 29

Introduction

Attracting vs. Entrapping

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 30

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content:

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 31

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 32

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Question

Which of these do you use daily?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 33

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Question

Which of these do you use daily?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 34

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Question

Which of these do you use daily?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 35

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Question

Which of these do you use daily? Hourly?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 36

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Question

Which of these do you use daily? Hourly?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 37

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Definitions

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 38

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Definitions

Attracting sticky content

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 39

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Definitions

Attracting sticky content – attracts

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 40

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Definitions

Attracting sticky content – attracts Entrapping sticky content

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 41

Introduction

Attracting vs. Entrapping

Recall our examples of sticky content: news/weather updates horoscopes webmail

  • nline games

Definitions

Attracting sticky content – attracts Entrapping sticky content – attracts AND entraps

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 4 / 17

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SLIDE 42

Introduction

Road Map

We will...

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 5 / 17

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SLIDE 43

Introduction

Road Map

We will... Model sticky content

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 5 / 17

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SLIDE 44

Introduction

Road Map

We will... Model sticky content

Based upon Katona and Sarvary (2009)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 5 / 17

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SLIDE 45

Introduction

Road Map

We will... Model sticky content

Based upon Katona and Sarvary (2009)

Discuss effects of sticky content

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 5 / 17

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SLIDE 46

Introduction

Road Map

We will... Model sticky content

Based upon Katona and Sarvary (2009)

Discuss effects of sticky content

Attracting

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 5 / 17

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SLIDE 47

Introduction

Road Map

We will... Model sticky content

Based upon Katona and Sarvary (2009)

Discuss effects of sticky content

Attracting Entrapping

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 5 / 17

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SLIDE 48

Introduction

Road Map

We will... Model sticky content

Based upon Katona and Sarvary (2009)

Discuss effects of sticky content

Attracting Entrapping

Conclude

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 5 / 17

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SLIDE 49

The Model

The Internet

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 6 / 17

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SLIDE 50

The Model

The Internet

Two parties of interest

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 6 / 17

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SLIDE 51

The Model

The Internet

Two parties of interest Content providers (“sites”)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 6 / 17

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SLIDE 52

The Model

The Internet

Two parties of interest Content providers (“sites”) Consumers

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 6 / 17

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SLIDE 53

The Model

The Internet

Two parties of interest Content providers (“sites”) – finitely many, n Consumers

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 6 / 17

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SLIDE 54

The Model

The Internet

Two parties of interest Content providers (“sites”) – finitely many, n Consumers – measure 1

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 6 / 17

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SLIDE 55

The Model

Sites

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 56

The Model

Sites

Parameters...

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 57

The Model

Sites

Parameters... commercial content parameter ci ∈ [0, 1]

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 58

The Model

Sites

Parameters... commercial content parameter ci ∈ [0, 1] (sale value)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 59

The Model

Sites

Parameters... commercial content parameter ci ∈ [0, 1] (sale value) sticky content parameter si

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 60

The Model

Sites

Parameters... commercial content parameter ci ∈ [0, 1] (sale value) sticky content parameter si ...and links

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 61

The Model

Sites

Parameters... commercial content parameter ci ∈ [0, 1] (sale value) sticky content parameter si ...and links sold in a market

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 62

The Model

Sites

Parameters... commercial content parameter ci ∈ [0, 1] (sale value) sticky content parameter si ...and links sold in a market

qi := per-click price of a link from site i

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 63

The Model

Sites

Parameters... commercial content parameter ci ∈ [0, 1] (sale value) sticky content parameter si ...and links sold in a market

qi := per-click price of a link from site i (∂qi

∂ci > 0)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 7 / 17

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SLIDE 64

The Model

Consumers

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 65

The Model

Consumers

Measure 1 of consumers

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 66

The Model

Consumers

Measure 1 of consumers browse the web

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 67

The Model

Consumers

Measure 1 of consumers browse the web

Question

How can we track consumer traffic?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 68

The Model

Consumers

Measure 1 of consumers browse the web

Question

How can we track consumer traffic?

Answer

PageRank!

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 69

The Model

Consumers

Measure 1 of consumers browse the web

Question

How can we track consumer traffic?

Answer

PageRank!

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 70

The Model

Consumers

Measure 1 of consumers randomly walk the web

Question

How can we track consumer traffic?

Answer

PageRank!

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 71

The Model

Consumers

Measure 1 of consumers randomly walk the web

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 72

The Model

Consumers

Measure 1 of consumers randomly walk the web, buying content from the sites they visit

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 73

The Model

Consumers

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 74

The Model

Consumers

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 8 / 17

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SLIDE 75

The Model Attracting Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 9 / 17

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SLIDE 76

The Model Attracting Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness:

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 9 / 17

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SLIDE 77

The Model Attracting Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 9 / 17

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SLIDE 78

The Model Attracting Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 9 / 17

slide-79
SLIDE 79

The Model Attracting Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M := (Mij)1≤i,j≤n

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 9 / 17

slide-80
SLIDE 80

The Model Attracting Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M := (Mij)1≤i,j≤n, where Mij =     

1 dout

i

+1

i = j,

1 dout

i

+1

i → j, i → j.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 9 / 17

slide-81
SLIDE 81

The Model Attracting Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M := (Mij)1≤i,j≤n, where Mij =     

1 dout

i

+1

i = j,

1 dout

i

+1

i → j, i → j. r (t+1) = δ · r (t) · M + (1 − δ) · r (0)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 9 / 17

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SLIDE 82

The Model Attracting Sticky Content

Remarks

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 10 / 17

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SLIDE 83

The Model Attracting Sticky Content

Remarks

In the case si ≡ s

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 10 / 17

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SLIDE 84

The Model Attracting Sticky Content

Remarks

In the case si ≡ s, r (0) = 1

n, . . . , 1 n

  • .

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 10 / 17

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SLIDE 85

The Model Attracting Sticky Content

Remarks

In the case si ≡ s, r (0) = 1

n, . . . , 1 n

  • .

We recover the model of Katona and Sarvary (Marketing Science, 2009).

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 10 / 17

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SLIDE 86

Results Attracting Sticky Content

Equilibrium Results

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

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SLIDE 87

Results Attracting Sticky Content

Equilibrium Results

Proposition

Set of network equilibria is independent of sticky content distribution.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

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SLIDE 88

Results Attracting Sticky Content

Equilibrium Results

Proposition

Set of network equilibria is independent of sticky content distribution.

Corollary

In equilibrium, out-degree weakly decreases in ci.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

slide-89
SLIDE 89

Results Attracting Sticky Content

Equilibrium Results

Proposition

Set of network equilibria is independent of sticky content distribution.

Corollary

In equilibrium, out-degree weakly decreases in ci.

Corollary

In equilibrium, in-degree and limit traffic increase in ci.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

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SLIDE 90

Results Attracting Sticky Content

Equilibrium Results

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

slide-91
SLIDE 91

Results Attracting Sticky Content

Equilibrium Results

Corollary

Attracting sticky content is strictly beneficial for sites.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

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SLIDE 92

Results Attracting Sticky Content

Equilibrium Results

Corollary

Attracting sticky content is strictly beneficial for sites.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

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SLIDE 93

Results Attracting Sticky Content

Equilibrium Results

Corollary

Attracting sticky content is strictly beneficial for sites.

And now for something...

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

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SLIDE 94

Results Attracting Sticky Content

Equilibrium Results

Corollary

Attracting sticky content is strictly beneficial for sites.

And now for something... ...surprisingly different.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 11 / 17

slide-95
SLIDE 95

The Model Entrapping Sticky Content Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 12 / 17

slide-96
SLIDE 96

The Model Entrapping Sticky Content

Consumers (Attracting Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M := (Mij)1≤i,j≤n, where Mij =     

1 dout

i

+1

i = j,

1 dout

i

+1

i → j, i → j. r (t+1) = δ · r (t) · M + (1 − δ) · r (0)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 12 / 17

slide-97
SLIDE 97

The Model Entrapping Sticky Content

Consumers (Entrapping Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M := (Mij)1≤i,j≤n, where Mij =     

1 dout

i

+1

i = j,

1 dout

i

+1

i → j, i → j. r (t+1) = δ · r (t) · M + (1 − δ) · r (0)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 12 / 17

slide-98
SLIDE 98

The Model Entrapping Sticky Content

Consumers (Entrapping Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M := (Mij)1≤i,j≤n, where Mij =     

si dout

i

+si

i = j,

1 dout

i

+si

i → j, i → j. r (t+1) = δ · r (t) · M + (1 − δ) · r (0)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 12 / 17

slide-99
SLIDE 99

The Model Entrapping Sticky Content

Consumers (Entrapping Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M := (Mij)1≤i,j≤n, where Mij =     

si dout

i

+si

i = j,

1 dout

i

+si

i → j, i → j. r (t+1) = δ · r (t) · M + (1 − δ) · r (0)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 12 / 17

slide-100
SLIDE 100

The Model Entrapping Sticky Content

Consumers (Entrapping Sticky Content)

Measure 1 of consumers randomly walk the web, buying content from the sites they visit with probability 1

Starting distribution depends on stickiness: r (0) = s1 S , . . . , sn S

  • ,

where S = n

i=1 si.

Transition matrix is M′ := (M′

ij)1≤i,j≤n, where

M′

ij =

    

si dout

i

+si

i = j,

1 dout

i

+si

i → j, i → j. r (t+1) = δ · r (t) · M′ + (1 − δ) · r (0)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 12 / 17

slide-101
SLIDE 101

The Model Entrapping Sticky Content

Remarks

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 13 / 17

slide-102
SLIDE 102

The Model Entrapping Sticky Content

Remarks

In the case si ≡ 1

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 13 / 17

slide-103
SLIDE 103

The Model Entrapping Sticky Content

Remarks

In the case si ≡ 1, r (0) = 1

n, . . . , 1 n

  • .

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 13 / 17

slide-104
SLIDE 104

The Model Entrapping Sticky Content

Remarks

In the case si ≡ 1, r (0) = 1

n, . . . , 1 n

  • and M′ = M.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 13 / 17

slide-105
SLIDE 105

The Model Entrapping Sticky Content

Remarks

In the case si ≡ 1, r (0) = 1

n, . . . , 1 n

  • and M′ = M.

We again recover the model of Katona and Sarvary (2009) as a special case.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 13 / 17

slide-106
SLIDE 106

The Model Entrapping Sticky Content

Remarks

In the case si ≡ 1, r (0) = 1

n, . . . , 1 n

  • and M′ = M.

We again recover the model of Katona and Sarvary (2009) as a special case. However, we do not recover any other cases of the attracting content model.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 13 / 17

slide-107
SLIDE 107

Results Entrapping Sticky Content

Key Result

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-108
SLIDE 108

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content...

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-109
SLIDE 109

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content...

Proposition

We have ∂s∗

i

∂ci > 0.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-110
SLIDE 110

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-111
SLIDE 111

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-112
SLIDE 112

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-113
SLIDE 113

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

1

s∗

i is well-defined when Ri ≤ (dout

i

)2 S

.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-114
SLIDE 114

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

1

s∗

i is well-defined when Ri ≤ (dout

i

)2 S

.

2

For any i such that Ri ≤ (dout

i

)2 S

, we have ∂s∗

i

∂ci > 0.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-115
SLIDE 115

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

1

s∗

i is well-defined when Ri ≤ (dout

i

)2 S

.

2

For any i such that Ri ≤ (dout

i

)2 S

, we have ∂s∗

i

∂ci > 0.

3

As Ri → (dout

i

)2 S

, we have ∂s∗

i

∂ci → 0.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-116
SLIDE 116

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-117
SLIDE 117

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

For Ri < (dout

i

)2 S

sufficiently large, site i would prefer not to have entrapping sticky content.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-118
SLIDE 118

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

For Ri < (dout

i

)2 S

sufficiently large, site i would prefer not to have entrapping sticky content.

This is different from the result for attracting content!

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-119
SLIDE 119

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

For Ri < (dout

i

)2 S

sufficiently large, site i would prefer not to have entrapping sticky content.

This is different from the result for attracting content! But notice that this is an ex post comparative static....

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-120
SLIDE 120

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

For Ri < (dout

i

)2 S

sufficiently large, site i would prefer not to have entrapping sticky content.

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-121
SLIDE 121

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

For Ri < (dout

i

)2 S

sufficiently large, site i would prefer not to have entrapping sticky content.

This implies endogenous business model specialization

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-122
SLIDE 122

Results Entrapping Sticky Content

Key Result

If s∗

i is site i’s optimal level of entrapping sticky

content and Ri :=

j→i rj S(dout

j

+sj)

(rj = limt→∞ r (t)

j

)

Proposition

For Ri < (dout

i

)2 S

sufficiently large, site i would prefer not to have entrapping sticky content.

This implies endogenous business model specialization Entrapping content ⇐ ⇒ Little inlink traffic

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 14 / 17

slide-123
SLIDE 123

Conclusion

Summary of Results

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 15 / 17

slide-124
SLIDE 124

Conclusion

Summary of Results

attracting sticky content is always desired

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 15 / 17

slide-125
SLIDE 125

Conclusion

Summary of Results

attracting sticky content is always desired entrapping sticky content is sometimes desired

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 15 / 17

slide-126
SLIDE 126

Conclusion

Summary of Results

attracting sticky content is always desired entrapping sticky content is sometimes desired ... by site owners

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 15 / 17

slide-127
SLIDE 127

Conclusion

Possible Extensions

attracting sticky content is always desired entrapping sticky content is sometimes desired ... by site owners

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 15 / 17

slide-128
SLIDE 128

Conclusion

Possible Extensions

attracting sticky content is always desired entrapping sticky content is sometimes desired ... by site owners What about consumers?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 15 / 17

slide-129
SLIDE 129

Conclusion

Possible Extensions

What about consumers?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 16 / 17

slide-130
SLIDE 130

Conclusion

Possible Extensions

What about consumers? Effects on Price Levels

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 16 / 17

slide-131
SLIDE 131

Conclusion

Possible Extensions

What about consumers? Effects on Price Levels

Can we sign ∂qi

∂si ?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 16 / 17

slide-132
SLIDE 132

Conclusion

Possible Extensions

What about consumers? Effects on Price Levels

Can we sign ∂qi

∂si ?

Reference Links

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 16 / 17

slide-133
SLIDE 133

Conclusion

Possible Extensions

What about consumers? Effects on Price Levels

Can we sign ∂qi

∂si ?

Reference Links

Addressed briefly by Katona and Sarvary (2009)

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 16 / 17

slide-134
SLIDE 134

Conclusion

Possible Extensions

What about consumers? Effects on Price Levels

Can we sign ∂qi

∂si ?

Reference Links

Addressed briefly by Katona and Sarvary (2009)

Non-commercial sites?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 16 / 17

slide-135
SLIDE 135

Conclusion

Possible Extensions

What about consumers? Effects on Price Levels

Can we sign ∂qi

∂si ?

Reference Links

Addressed briefly by Katona and Sarvary (2009)

Non-commercial sites? Update the Wikipedia page?

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 16 / 17

slide-136
SLIDE 136

Conclusion QED

Questions?

kominers@fas.harvard.edu

Scott Duke Kominers (Harvard) NetEcon’09 – July 7, 2009 17 / 17