This Talk We give a simple allocation and pricing mechanism whose - - PowerPoint PPT Presentation

▶
this talk
SMART_READER_LITE
LIVE PREVIEW

This Talk We give a simple allocation and pricing mechanism whose - - PowerPoint PPT Presentation

Dec 10, 2022 299 likes •1.69k views

This Talk We give a simple allocation and pricing mechanism whose Nash equilibrium solves a very large optimization problem This Talk We give a simple allocation and pricing mechanism whose Nash equilibrium solves a very large optimization

slide-1
SLIDE 1
slide-2
SLIDE 2

We give a simple allocation and pricing mechanism whose Nash equilibrium solves a very large

  • ptimization problem

This Talk

slide-3
SLIDE 3

We give a simple allocation and pricing mechanism whose Nash equilibrium solves a very large

  • ptimization problem

Very Large = over the infjnite results of a search engine.

This Talk

slide-4
SLIDE 4

Outline

  • A Introduction to Sponsored Search

– Bids, Impressions, Click-Through Rate, Advertizers, Platform

  • Auction or Optimize?

– Our Mechanism, Generalized 2nd Price, VCG Mechanism, Decomposition.

  • Our Results

– Main Theorem, Implementations

  • Further Results and Extensions

– Dynamics, Multivariate Utilities, General Page Layouts, Budgets.

slide-5
SLIDE 5

Introduction to Sponsored Search

slide-6
SLIDE 6

Sponsored Search

slide-7
SLIDE 7

Sponsored Search

slide-8
SLIDE 8

Sponsored Search

Ads Ads

slide-9
SLIDE 9

Sponsored Search

slide-10
SLIDE 10

Sponsored Search

slide-11
SLIDE 11

Sponsored Search

slide-12
SLIDE 12

Sponsored Search

slide-13
SLIDE 13

Sponsored Search

Bid

slide-14
SLIDE 14

Sponsored Search

Bid Impressions

slide-15
SLIDE 15

Sponsored Search

Bid Impressions Price per click

slide-16
SLIDE 16

Sponsored Search

✓

slide-17
SLIDE 17

Sponsored Search

✓

Click

slide-18
SLIDE 18

Sponsored Search

✓

slide-19
SLIDE 19

Variability in Sponsored Search

A one-shot or repeated auction:

  • eg. “Dominos Pizza”

(exact match)

CTR BID 0.10 0.05 6 4 2

slide-20
SLIDE 20

Variability in Sponsored Search

A mixture of auctions:

  • eg. “ … Dominos … Pizza …”

(phrase match)

CTR BID 0.10 0.05 6 4 2

slide-21
SLIDE 21

Variability in Sponsored Search

A bigger mixture of auctions:

  • eg. “ … Delivery … Pizza …”

(broad match)

CTR BID 0.10 0.05 6 4 2

slide-22
SLIDE 22

Variability in Sponsored Search

A continuum of auctions:

  • eg. “ … Delivery … Pizza …” + location + time

(broad match) + Searcher

CTR BID 0.10 0.05 6 4 2

slide-23
SLIDE 23

Information and Temporal Asymmetry

slide-24
SLIDE 24

Information and Temporal Asymmetry

The Searcher

slide-25
SLIDE 25

Information and Temporal Asymmetry

The Searcher The Platform

slide-26
SLIDE 26

Information and Temporal Asymmetry

The Searcher The Platform

The Advertiser

slide-27
SLIDE 27

Information and Temporal Asymmetry

The Searcher The Platform

The Advertiser

Search Distribution

slide-28
SLIDE 28

Information and Temporal Asymmetry

The Searcher The Platform

The Advertiser

Search Distribution When a search occurs Click-Through Assignment

slide-29
SLIDE 29

Information and Temporal Asymmetry

The Searcher The Platform

The Advertiser

Search Distribution When a search occurs Click-Through Assignment Receives average information Click-Through Assignment

slide-30
SLIDE 30

Information and Temporal Asymmetry

The Searcher The Platform

The Advertiser

Search Distribution Unknown To everyone When a search occurs Click-Through Assignment Receives average information Click-Through Assignment

slide-31
SLIDE 31

Information and Temporal Asymmetry

The Searcher The Platform

The Advertiser

Search Distribution Unknown To everyone When a search occurs Click-Through Assignment Platform knows Advertiser doesn't Receives average information Click-Through Assignment

slide-32
SLIDE 32

Information and Temporal Asymmetry

The Searcher The Platform

The Advertiser

Search Distribution Unknown To everyone When a search occurs Click-Through Assignment Platform knows Advertiser doesn't Receives average information Click-Through Assignment Platform knows Advertiser knows

slide-33
SLIDE 33

Auction or Optimize?

slide-34
SLIDE 34

Two Auctions

– Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l

slide-35
SLIDE 35

Two Auctions

– Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l

Auction 1:

slide-36
SLIDE 36

Two Auctions

Assign – Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l in order

Auction 1:

slide-37
SLIDE 37

Two Auctions

Assign Pay, per-click – Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l in order

Auction 1:

slide-38
SLIDE 38

Two Auctions

Assign Pay, per-click – Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l in order

Auction 1: Auction 2:

slide-39
SLIDE 39

Two Auctions

Assign Pay, per-click – Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l Assign max matching in order

Auction 1: Auction 2:

slide-40
SLIDE 40

Two Auctions

Assign Pay, per-click – Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l Assign max matching Pay, per-click in order

Auction 1: Auction 2:

slide-41
SLIDE 41

Two Auctions

Assign Pay, per-click – Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l Assign max matching Pay, per-click in order

Auction 1: Auction 2: Generalized 2nd Price

slide-42
SLIDE 42

Two Auctions

Assign Pay, per-click – Bid of ad i – Search Type – CTR given bids – Click-Through ad i slot l Assign max matching Pay, per-click in order

Auction 1: Auction 2: Generalized 2nd Price A VCG Auction

slide-43
SLIDE 43

Immediate Advantages

slide-44
SLIDE 44

Immediate Advantages

slide-45
SLIDE 45

Immediate Advantages

There is not ordering of Ads!

Generalized 2nd Price Breaks down. Our mechanism and results hold true.

slide-46
SLIDE 46

Is it GSP or VCG?

slide-47
SLIDE 47

Is it GSP or VCG?

Google (2006) said:

“Google’s unique auction model uses Nobel Prize winning economic theory … the AdWords™ Discounter makes sure that they only pay what they need in order to stay ahead

  • f their nearest competitor.”
slide-48
SLIDE 48

Is it GSP or VCG?

Google (2006) said:

“Google’s unique auction model uses Nobel Prize winning economic theory … the AdWords™ Discounter makes sure that they only pay what they need in order to stay ahead

  • f their nearest competitor.”
  • Q. Is this really true?
slide-49
SLIDE 49

Is it GSP or VCG?

Google (2006) said:

“Google’s unique auction model uses Nobel Prize winning economic theory … the AdWords™ Discounter makes sure that they only pay what they need in order to stay ahead

  • f their nearest competitor.”
  • Q. Is this really true?
  • A. Not really.
slide-50
SLIDE 50

Is it GSP or VCG?

Google (2006) said:

“Google’s unique auction model uses Nobel Prize winning economic theory … the AdWords™ Discounter makes sure that they only pay what they need in order to stay ahead

  • f their nearest competitor.”
  • Q. What did they really mean?
  • Q. Is this really true?
  • A. Not really.
slide-51
SLIDE 51

Is it GSP or VCG?

Google (2006) said:

“Google’s unique auction model uses Nobel Prize winning economic theory … the AdWords™ Discounter makes sure that they only pay what they need in order to stay ahead

  • f their nearest competitor.”
  • Q. What did they really mean?
  • A. The VCG Mechanism...
  • Q. Is this really true?
  • A. Not really.

Vickrey Clark Groves

slide-52
SLIDE 52

The VCG Mechanism

slide-53
SLIDE 53

The VCG Mechanism

  • Advertiser's utilities
slide-54
SLIDE 54

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
slide-55
SLIDE 55

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints
slide-56
SLIDE 56

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns:

slide-57
SLIDE 57

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns:

Maximize Value

slide-58
SLIDE 58

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns:

slide-59
SLIDE 59

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns: Platform Prices:

slide-60
SLIDE 60

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns: Platform Prices:

Everyone else's value

slide-61
SLIDE 61

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns: Platform Prices:

Everyone else's value Value without you there

slide-62
SLIDE 62

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns: Platform Prices:

slide-63
SLIDE 63

The VCG Mechanism

  • Advertiser's utilities
  • bid utilities
  • Assignment constraints

Platform Assigns: Platform Prices: Equilibrium Advertizer:

slide-64
SLIDE 64

The VCG Mechanism

Theorem

The VCG mechanism has a dominate strategies equilibrium that is:

slide-65
SLIDE 65

The VCG Mechanism

Theorem

The VCG mechanism has a dominate strategies equilibrium that is:

– Incentive compatible

slide-66
SLIDE 66

The VCG Mechanism

Theorem

The VCG mechanism has a dominate strategies equilibrium that is:

– Incentive compatible – Effjcient

slide-67
SLIDE 67

Directly Applying VCG

slide-68
SLIDE 68

Directly Applying VCG

Pros

  • 1. Result applies in very general settings
  • 2. Allocation of Adverts is provably optimal
slide-69
SLIDE 69

Directly Applying VCG

Pros

  • 1. Result applies in very general settings
  • 2. Allocation of Adverts is provably optimal

Cons

  • 1. Advertisers submit their entire utility function
slide-70
SLIDE 70

Directly Applying VCG

Pros

  • 1. Result applies in very general settings
  • 2. Allocation of Adverts is provably optimal

Cons

  • 1. Advertisers submit their entire utility function
  • 2. Utility isn't for a single adauction but for all adauctions
slide-71
SLIDE 71

Directly Applying VCG

Pros

  • 1. Result applies in very general settings
  • 2. Allocation of Adverts is provably optimal

Cons

  • 1. Advertisers submit their entire utility function
  • 2. Utility isn't for a single adauction but for all adauctions
  • 3. Platform needs to solve a massive optimization
slide-72
SLIDE 72

Directly Applying VCG

Pros

  • 1. Result applies in very general settings
  • 2. Allocation of Adverts is provably optimal

Cons

  • 1. Advertisers submit their entire utility function
  • 2. Utility isn't for a single adauction but for all adauctions
  • 3. Platform needs to solve a massive optimization

This talk: We deal with these issue by appropriately decomposing this massive optimization.

slide-73
SLIDE 73

A Massive Optimization

slide-74
SLIDE 74

A Massive Optimization

Max Utility

slide-75
SLIDE 75

A Massive Optimization

Max Utility Mean click-rate

slide-76
SLIDE 76

A Massive Optimization

Max Utility Mean click-rate Per impression Assignment Constraints

slide-77
SLIDE 77

A Massive Optimization

Max Utility Mean click-rate Per impression Assignment Constraints small

slide-78
SLIDE 78

A Massive Optimization

Max Utility Mean click-rate Per impression Assignment Constraints small Large!

slide-79
SLIDE 79

A Massive Optimization

Max Utility Mean click-rate Per impression Assignment Constraints small Large! Uncountably infjnite!!

slide-80
SLIDE 80

A Massive Optimization

  • even if we knew all the parameters, it's impossible to

solve this optimization ofg-line

slide-81
SLIDE 81

A Massive Optimization

  • even if we knew all the parameters, it's impossible to

solve this optimization ofg-line

  • Still … maybe we can solve a lot of small optimizations...
slide-82
SLIDE 82

A Small Optimization

When a search occurs, solve:

slide-83
SLIDE 83

A Small Optimization

When a search occurs, solve: Assignment Problem

slide-84
SLIDE 84

A Small Optimization

When a search occurs, solve: Assignment Problem

slide-85
SLIDE 85

A Small Optimization

When a search occurs, solve:

Lots of polynomial time algorithms:

Assignment Problem

slide-86
SLIDE 86

A Small Optimization

When a search occurs, solve:

Lots of polynomial time algorithms:

Hungarian ; Hopcroft-Karp ; Bertsekas' Auction ...

Assignment Problem

slide-87
SLIDE 87

Optimization Decomposition

Solve the big optimization with many little optimizations

slide-88
SLIDE 88

Optimization Decomposition

  • 1. Substitution:

Solve the big optimization with many little optimizations

slide-89
SLIDE 89

Optimization Decomposition

  • 1. Substitution:
  • 2. Separability:

Solve the big optimization with many little optimizations

slide-90
SLIDE 90

Optimization Decomposition

  • 1. Substitution:
  • 2. Separability:

MAIN IDEA: Substitute utility for Separate out the resulting optimization

Solve the big optimization with many little optimizations

slide-91
SLIDE 91

Optimization Decomposition

  • 1. Substitution:
  • 2. Separability:

MAIN IDEA: Substitute utility for Separate out the resulting optimization THE RESULT: A massively distributed VCG Mechanism

Solve the big optimization with many little optimizations

slide-92
SLIDE 92

Our Results

slide-93
SLIDE 93

A Preliminary Calculation

slide-94
SLIDE 94

A Preliminary Calculation

slide-95
SLIDE 95

A Preliminary Calculation

slide-96
SLIDE 96

A Preliminary Calculation

LF-Transform Assignment Problem

slide-97
SLIDE 97

A Preliminary Optimization Result

slide-98
SLIDE 98

A Preliminary Optimization Result

To solve the Massive Optimization

slide-99
SLIDE 99

A Preliminary Optimization Result

To solve the Massive Optimization Advertiser's must signal average prices

slide-100
SLIDE 100

A Preliminary Optimization Result

To solve the Massive Optimization Advertiser's must signal average prices Platform solves Assignment when each search occurs

slide-101
SLIDE 101

A Preliminary Optimization Result

Advertiser's must signal average prices Platform solves Assignment when each search occurs

slide-102
SLIDE 102

A Preliminary Optimization Result

Advertiser's must signal average prices Platform solves Assignment when each search occurs

  • Decomposed on the timescales of Platform and Advertisers.
slide-103
SLIDE 103

A Preliminary Optimization Result

Advertiser's must signal average prices Platform solves Assignment when each search occurs

  • Decomposed on the timescales of Platform and Advertisers.
  • Search distribution is not required.
slide-104
SLIDE 104

A Preliminary Optimization Result

Advertiser's must signal average prices Platform solves Assignment when each search occurs

  • Decomposed on the timescales of Platform and Advertisers.
  • Search distribution is not required.
  • But it's an optimization result, we must incentivize this behaviour.
slide-105
SLIDE 105

Main Theorem and Mechanism Design

slide-106
SLIDE 106

Main Theorem and Mechanism Design

Advertizers maximizes rewards:

slide-107
SLIDE 107

Main Theorem and Mechanism Design

Advertizers maximizes rewards: A Nash Equilibrium is then:

slide-108
SLIDE 108

Main Theorem and Mechanism Design

Advertizers maximizes rewards: A Nash Equilibrium is then:

slide-109
SLIDE 109

Main Theorem and Mechanism Design

Advertizers maximizes rewards: A Nash Equilibrium is then:

These Prices

slide-110
SLIDE 110

Main Theorem and Mechanism Design

Advertizers maximizes rewards: A Nash Equilibrium is then:

These Prices at Nash Equilibrium

slide-111
SLIDE 111

Main Theorem and Mechanism Design

Advertizers maximizes rewards: A Nash Equilibrium is then:

These Prices at Nash Equilibrium solve the Massive Optimization

slide-112
SLIDE 112

Proof of Main Theorem

Optimality condition for the dual:

envelope thrm Fenchel- Moreau thrm Substitute integrate

slide-113
SLIDE 113

Proof of Main Theorem

Optimality condition for the dual:

envelope thrm Fenchel- Moreau thrm Substitute

The correct price!!

integrate

slide-114
SLIDE 114

How to Implement the Prices

slide-115
SLIDE 115

How to Implement the Prices

Two Price Implementations:

slide-116
SLIDE 116

How to Implement the Prices

  • 1. Let

and price Two Price Implementations:

slide-117
SLIDE 117

How to Implement the Prices

  • 1. Let

and price

  • 2. A discounted-VCG price

Two Price Implementations:

slide-118
SLIDE 118

How to Implement the Prices

  • 1. Let

and price

  • 2. A discounted-VCG price

Two Price Implementations: the same average price

slide-119
SLIDE 119

How to Implement the Prices

  • 1. Let

and price

  • 2. A discounted-VCG price

Two Price Implementations: the same average price

slide-120
SLIDE 120

A massively distributed VCG mechanism

slide-121
SLIDE 121

A very simple pay-per click mechanism:

A massively distributed VCG mechanism

slide-122
SLIDE 122

A very simple pay-per click mechanism: Assignment Pricing

A massively distributed VCG mechanism

slide-123
SLIDE 123

A very simple pay-per click mechanism: Assignment Pricing at Nash equilibrium solves the Massive Optimization

A massively distributed VCG mechanism

slide-124
SLIDE 124

Further Results and Extensions

slide-125
SLIDE 125

Dynamics and Convergence

slide-126
SLIDE 126

Dynamics and Convergence

A natural dynamic:

slide-127
SLIDE 127

Dynamics and Convergence

A natural dynamic: Lyapunov function:

slide-128
SLIDE 128

Dynamics and Convergence

A natural dynamic: Lyapunov function:

slide-129
SLIDE 129

Dynamics and Convergence

A natural dynamic: Lyapunov function:

slide-130
SLIDE 130

Further Extensions

Controlling number of slots:

slide-131
SLIDE 131

Further Extensions

Multivariate utilities:

slide-132
SLIDE 132

Further Extensions

Budget constraints:

slide-133
SLIDE 133

Summary of the talk

slide-134
SLIDE 134

Summary of the talk

  • Massively decomposed VCG implementation

– Simple – Flexible

slide-135
SLIDE 135

Summary of the talk

  • Massively decomposed VCG implementation

– Simple – Flexible

  • Can be Implemented

– Relevant timescale – Relevant information asymmetry – Low Computational Overhead – Applies to difgerent page layouts

slide-136
SLIDE 136

Summary of the talk

  • Massively decomposed VCG implementation

– Simple – Flexible

  • Can be Implemented

– Relevant timescale – Relevant information asymmetry – Low Computational Overhead – Applies to difgerent page layouts

  • Provably solves an Infjnitely Large Optimization.
slide-137
SLIDE 137

Thank you for listening!