Sponsored Search Markets (from Networks, Crowds, and Markets: Reasoning About a Highly Connected World)

Chapter 15 Sponsored Search Markets from Networks, Crowds, and Markets: Reasoning About a

Highly Connected World

Junpei Kawamoto

Reading seminar

http://www.cs.cornell.edu/home/kleinber/networks-book/





Advertising Tied to Search Behavior

Chapter 15 - Sponsored Search Markets 2

Search engine meets search advertising

Early advertising was sold on the basis of “impression” like

magazine or newspapers ad.

It was not efficient way

Showing ad of calligraphy pens to all people vs. to people searching

“calligraphy pen”.

Search engine queries are potent way to get users to express

their intent.

Keywords-bases advertisement.

How to sell keywords-based ad?

Advertising Tied to Search Behavior

Paying per click

Cost-per-click (CPC) model

You only pay when a user actually clicks on the ad.

Clicking on an ad represents an even stronger indication of

intent than simply issuing a query.

Setting prices through an auction

How should a search engine set the prices pre click for

different queries?

One easy way is the search engine posts prices.

However, there are lots of queries and impossible to decide prices for

those all queries.

Auction protocols is a good way to decide prices.


Overview


1. Advertising as a Matching Market

2. Encouraging Truthful Bidding

in Matching markets: The VCG Principle

3. Analyzing the VCG Procedure:

Truth-Telling as a Dominant Strategy

4. The Generalized Second Price Auction

5. Equilibria of the Generalized Second Price Auction

6. Ad Quality

7. Complex Queries and Interactions Among Keywords

Advertising as a Matching Market

Click through Rates and Revenues Per Click.

a

b

c

x

y

z

slots advertisers click through

rates

10

5

2

revenues

per click

3

2

1




a

b

c

x

y

z


rates

10

5

2

revenues

per click

3

2

1

Click through rates: e.g. # of clicks per hour.

Assuming:

1. Advertisers know the click through rates;

2. Click through rates depend only on slot not contents of the ads;

3. Click through rates don’t depend on ads on other slots.




a

b

c

x

y

z


rates

10

5

2

revenues

per click

3

2

1


The expected amount of revenues advertisers receive per user clicking on the ad.

Assuming:

1. These values are intrinsic to the advertisers,

2. doesn’t depend on what was being shown on the page.



Constructing a Matching Market

The participants in a matching market consists of a set of

buyers and a set of sellers.

Each buyer j has a valuation for the item offered by each seller

i. This valuation can depend on the identities of both the buyer

and the seller, and we denote vij.

The goal is to match up buyers with sellers, in such a way that

no buyers purchases two different items, and the same item

isn’t sold two different buyers.

The basic ingredients of matching market from Chapter 10.




ri: the click through rate of slot i

vj: the revenue per click of advertiser j

vij = rivj: the benefit advertiser j receives from an ad in slot i

Slots = Sellers

Advertisers = Buyer

Advertiser j’s valuation for slot i in the language of matching market,

The problem is to assign sellers to buyers in a matching market.



a

b

c

x

y

z


rates

10

5

2

revenues

per click

3

2

1


valuations

30, 15, 6

20, 10, 4

10, 5, 2

Advertisers’ valuations for the slots



a

b

c

x

y

z


rates

10

5

2

revenues

per click

3

2

1


valuations

30, 15, 6

20, 10, 4

10, 5, 2


the benefit advertiser j receives from an ad in slot i, vij = rivj



a

b

c

x

y

z


rates

10

5

2

revenues

per click

3

2

1


valuations

30, 15, 6

20, 10, 4

10, 5, 2






That is a matching market with a special structure

The valuations of one buyer simply form a multiple of the valuations

of any other buyers.

Assumption:

# of slots = # of advertisers

If not, we can add fictitious slots or advertises.

The click through rates of fictitious slots = 0

The revenue pre clicks of fictitious advertises = 0



Obtaining Market-Clearing Prices

Each seller i announces a price pi for his item.

Each buyer j evaluates her payoff for choosing a particular seller i

it’s equal to the valuation minus the price for this seller’s item, vij – pi

We then build a perfect-seller graph by linking each buyers to the

seller or sellers from which she gets the highest payoff.

The prices are market-clearing if this graph has a perfect matching

in this case, we can assign distinct items to all the buyers in such a way

that each buyers gets an item that maximizes her payoff.

Using the framework from Chapter 10




Market-clearing prices exists for every matching market.

We have a procedure to construct market-clearing prices.

Market-clearing prices always maximizes the buyer’s total

valuations for the items they get.

From Chapter 10



a

b

c

x

y

z


rates

10

5

2

revenues

per click

3

2

1


valuations

30, 15, 6

20, 10, 4

10, 5, 2


Finally obtained the perfect-seller graph.



This construction of prices can only be carried out by

search engine if it actually knows the valuations of the

advertisers.

Next, we consider how to set prices in a setting where

the search engine doesn’t know these valuations; it must

rely on advertisers to report them without being able to

know whether this reporting is truthful.

Encouraging Truthful Bidding



What would be a good price-setting procedure when the search

engine doesn’t know advertises’ valuations?

In the early days, variants of the 1st-price auction used.

Recall from Chapter 9, in 1st-price auction, bidders under-report.

In the case of a single-item auction, 2nd-price auction is a solution.

Truthful bidding is a dominant strategy.

Avoid many of the pathologies associated with more complex auctions.

What is the analogue of the 2nd-price auction for advertising

markets with multiple slots?

How can we define a price-setting procedure for matching markets so

that truthful reporting of valuations is a dominant strategy for buyers?




The VCG Principle

How to generalize 2nd-price single-item auction to multi-item one.

A less obvious view of 2nd-price auction

The 2nd-price auction produces an allocation that maximizes social welfare.

The winner is charged an amount equal to the “harm” he causes the other

bidders by receiving the item.

1

2

n

v1

v2

vn

v1 > v2 > … > vn

Gets the apple




The VCG Principle






1

2

n

v1

v2

vn

v1 > v2 > … > vn

If bidder 1 weren’t present

Bidder 2 got the apple, which

was worth of v2

Nothing was changed for

bidder 3-n. (we ignore them)




The VCG Principle






1

2

n

v1

v2

vn

v1 > v2 > … > vn

The presence of bidder 1

causes the “harm” v2 to

bidder 2. (Bidder 2 lost an

item worthy of v2)

Therefore, bidder 1 must

pay v2 as the price of the

apple.




The VCG Principle






Vickrey-Clarke-Groves (VCG) principles




Applying the VCG Principles to Matching Markets

We have a set of buyers and sellers

# of buyers = # of sellers. (if not, we can add fictitious buyers and sellers.)

A buyer j has a valuation vij for the item i.

Each buyer knows only their own valuations.

Each buyer doesn’t care anyone else.

Procedure

Assign items to buyers so as to maximize total valuations.

Compute price with the VCG principles

independent, private values





a

b

c

x

y

z

slots advertisers price valuations

30, 15, 6

20, 10, 4

10, 5, 2

For example

30 for a, 15 for b, 6 for c





a

b

c

x

y

z


30, 15, 6

20, 10, 4

10, 5, 2

For example

If x weren’t present

y got slot a,

which was worthy of 20

z got slot b,

which was worthy of 5





a

b

c

x

y

z


30, 15, 6

20, 10, 4

10, 5, 2

For example

In fact, x is present.

y gets b, which is worthy of

10, instead of a, which is

worth of 20. Harm = 20-10

z gets c, which is worthy of

2, instead of b, which is






a

b

c

x

y

z


30, 15, 6

20, 10, 4

10, 5, 2

For example

In face, x is present.

y gets b, which is worthy of

10, instead of a, which is


z gets c, which is worthy of

2, instead of b, which is


10+3 = 13





a

b

c

x

y

z


30, 15, 6

20, 10, 4

10, 5, 2

For example

13

3

0





To generalize this pricing,

S: the set of sellers

B: the set of buyers

VSB: the maximum total valuations over all possible matching for S & B

S – i: the set of sellers without i

B – j: the set of buyers without j

VS-iB-j: the maximum total valuations of S-i & B-j

VCG price pij that we charge buyer j for item i

pij = VSB-j – VS-i

B-j

Total valuations if j

weren’t present

Total valuations in

such a case j gets i.




The VCG Price-Setting Procedure.

We assume there’s a single price-setting authority.

Collection information, assign items, and charge prices.

The Procedure

1. Ask buyers to announce valuations for items. (need truthful report)

2. Choose a socially optimal assignment of items to buyers. (can do it)

3. Charge each buyer the appropriate VCG price. (pij = VSB-j – VS-i

B-j)




Market-clearing price vs. VCG price.

Market-clearing price is a posted price, based on English

auction.

VCG price is a personalized price and based on 2nd-price

auction.

2nd-price auction vs. VCG prices

The basic idea is “harm-done-to-others” principle.

2nd-price auction for single item, VCG prices for multi items.

2nd-price auction is a VCG price auction.

Suppose 1 real item & n – 1 fictitious items.

Analyzing the VCG Procedure:



We’ll show the following claim.

If items are assigned and prices computed according to

the VCG procedure, then truthfully announcing valuations

is a dominant strategy for each buyer, and the resulting

assignment maximizes the total valuations of any perfect

matching of slots and advertisers.










obvious if buyers report their valuations truthfully, then the

assignment of items is designed to maximize the total

valuations by definition.










We’ll focus the first part.




Suppose when the buyer j announce her valuations

truthfully, then she is assigned to item i.

Buyer j’s payoff = vij – pij

If j lies, there’re two cases,

j lies but gets item i

her payoff won’t change because pij is independent with her bit.

j lies and gets item h

her payoff is vhj – phj

vij – pij = vij – (VSB-j – VS-i

B-j) = vij + VS-iB-j – VS

B-j = VSB – VS

B-j

vhj – phj = vhj – (VSB-j – VS-h

B-j) = vhj + VS-hB-j – VS

B-j ≤ VS

B – VSB-j

= VSB, because we assume

assignment j to i is optimal.

≤ VSB




Suppose when the buyer j announce her valuations

truthfully, then she is assigned to item i.

Buyer j’s payoff = vij – pij

If j lies, there’re two cases,

j lies but gets item i

her payoff won’t change because pij is independent with her bit.

j lies and gets item h

her payoff is vhj – phj

vij – pij = vij – (VSB-j – VS-i

B-j) = vij + VS-iB-j – VS

B-j = VSB – VS

B-j

vhj – phj = vhj – (VSB-j – VS-h

B-j) = vhj + VS-hB-j – VS

B-j ≤ VS

B – VSB-j

= VSB, because we assume

assignment j to i is optimal.

≤ VSB

vij – pij ≥ vhj – phj

That is, when the buyer j lies, her payoff become smaller or doesn’t change.

(no incentive to tell lie)




The VCG Procedure would make buyers happy.

But it’s not clear the VCG procedure is the best way to

generate revenue for the search engine.

Determining which procedure will maximize seller revenue is a

current research topic.

The Generalized Second Price Auction


the Generalized Second Price (GSP) auction (by Google)

a generalization of 2nd-price auction

it’s up to the advertiser whether they bit true valuations

a

b

c

x

y

z

slots advertisers price bids

b1

b2

bn-1

For example

b2

b3

bn

b1 > b2 > … > bn



GSP has a number of pathologies VCG avoids:

Truth-telling might not constitute a Nash equilibrium;

There can be multiple Nash equilibrium;

Some assignments don’t maximize the total valuations.

Good news

GSP has at least one Nash equilibrium,

Among them, there is one which maximize the total valuation.

However, how to maximize search engine’s revenue is a

still current research topic.



Truth-telling may not be an equilibrium.

a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1




a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1

price

10×6

4×1

0




a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1

payoff price

60

4

0

70 - 60

24 - 4

10×7




a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1

bid

5

6

1

x lies




a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1

bid

5

6

1

Changed




a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1

price

4 × 1

50

0

bid

5

6

1

x is the 2nd highest bidder so

use 3rd bid for the price




a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1

payoff price

4

50

0

28 - 4

24 - 4

bid

5

6

1




a

b

c

x

y

z


rates

10

4

0

revenues

per click

7

6

1

payoff price

4

50

0

28 - 4

24 - 4

bid

5

6

1

When x tell truth, his payoff = 70 – 60 = 10,

When x tell lie, his payoff = 28 – 4 = 24.

In this case, truth-telling is not an equilibrium.



Multiple and non-optimal equilibria.

a

b

c

x

y

z


rates

10

4

0

a

b

c

x

y

z


rates

10

4

0

bid

5

4

2

bid

3

5

1

Both are Nash equilibrium.




a

b

c

x

y

z


rates

10

4

0

a

b

c

x

y

z


rates

10

4

0

bid

5

4

2

bid

3

5

1

price payoff

40

8

0

70-40

24-8

0

revenues

per clicks

7

6

1




a

b

c

x

y

z


rates

10

4

0

a

b

c

x

y

z


rates

10

4

0

bid

5→3

4

2

bid

3

5

1

price payoff

8

30

0

28-8

60-30

0

revenues

per clicks

7

6

1

Less than when bid 5.

So not motivated bidding lower.




a

b

c

x

y

z


rates

10

4

0

a

b

c

x

y

z


rates

10

4

0

bid

5

4→6

2

bid

3

5

1

price payoff

8

50

0

28-8

60-50

0

revenues

per clicks

7

6

1

Less than when bid 4.

So not motivated bidding lower.




a

b

c

x

y

z


rates

10

4

0

a

b

c

x

y

z


rates

10

4

0

bid

5

4

2

bid

3

5

1

price payoff

40

8

0

70-40

24-8

0

revenues

per clicks

7

6

1

revenues

per clicks

7

6

1

price payoff

4

30

0

28-4

60-30

0




a

b

c

x

y

z


rates

10

4

0

a

b

c

x

y

z


rates

10

4

0

bid

5

4

2

bid

3

5

1

price payoff

40

8

0

70-40

24-8

0

revenues

per clicks

7

6

1

revenues

per clicks

7

6

1

price payoff

4

30

0

28-4

60-30

0

Total payoff

46

Total payoff

54



The Revenue of GSP and VCG

The search engine’s revenue is depend on which equilibrium is

selected.

a

b

c

x

y

z


rates

10

4

0

a

b

c

x

y

z

10

4

0

bid

5

4

2

3

5

1

price revenue

40

8

0

48

4

30

0

34

revenues

per clicks

7

6

1

7

6

1




VCG for the same example

a

b

c

x

y

z


rates

10

4

0

valuations revenues

per clicks

7

6

1

70, 28, 0

60, 24, 0

10, 4, 0

a

b

c

x

y

z

10

4

0

7

6

1

40

4

0

price revenue

44




Does GSP or VCG provide more revenue to the search

engine?

Ans.

It’s depend on which equilibrium of the GSP the advertises use.

Equilibria of the Generalized Second Price

Auction


GSP always has a Nash equilibrium

Assuming # of slots = # of advertisers

1

2

n

1

2

n

slots advertisers

Decreasing order of click

through rates

Decreasing order of

valuations per clicks

click through

rate

r1

r2

rn


Auction



Assuming # of slots = # of advertisers

1

2

n

1

2

n

slots advertisers

Obtaining Market-Clearing

Prices (from Chapter 10)

click through

rate

r1

r2

rn


Auction



Think about a set of matching market prices {p1, …, pn}

We can make them (from Chapter 10)

And think about a set of price per click

p*i = pi / ri (ri: click through rate)


Auction



p*1 ≥ p*2 ≥ … ≥ p*n

To see why that is true, we think p*j & p*k (j < k) (Goal: p*j ≤ p*k)

In slot k, total payoff is (vk – p*k)rk

In slot j, total payoff is (vk – p*j)rj

If rj > rk but slot k is preferred, then payoff of k ≥ payoff of j

(vk – p*k)rk ≥ (vk – p*

j)rj → vk – p*k ≥ vk – p*

j → p*j ≥ p*

k

If rk ≥ rj

pj ≥ pk → p*j ≥ p*

k


Auction



We simply have advertiser j place a bid of p*j-1

And advertiser 1 place any bid larger than p*1

1

2

n

1

2

n

slots advertisers bid

x (>p*1)

p*1

p*n-1


Auction



We simply have advertiser j place a bid of p*j-1

And advertiser 1 place any bid larger than p*1

1

2

n

1

2

n

slots advertisers price

p*1

p*2

p*n = 0

bid

x (>p*1)

p*1

p*n-1


Auction


Why do the bids form a Nash equilibrium?

Considering an advertise j in slot j,

If it were to lower its bid and move to slot k, then its price would be p*k

But since the prices are market-clearing, j is at least as happy with its

current slot at its current prices as it would be with k’s current slot at k’s

current price.

If the advertiser j bids higher and move to slot i, the bid = p*i

i i p*i+1 p*

i

price bid

i j p*i x > p*

i

price bid

i p*i+1 p*

i i+1

Advertiser j must pay higher that the

current price of slot i


Auction


Why do the bids form a Nash equilibrium?

Therefore the below bids is a Nash equilibrium

1

2

n

1

2

n

slots advertisers price

p*1

p*2

p*n= 0

bid

x (>p*1)

p*1

p*n-1

Ad Quality


The assumption of a fixed click through rate.

We assumed fixed click through rates rj

In practice, it’s also depend on the contents of ad.

Search engine worried about a low-quality advertiser bids

very highly.

The click through rate will be small.

The revenue of the search engine also will be small!

Ad Quality


The role of ad quality.

Uses an estimated ad quality factor qj for advertiser j.

The click through rate is qjri (instead of ri)

(if qi = 1 for all i, it is previous model we discussed. )

The valuations of advertiser j for slot i, vij = qjrivj

The bid bj of advertiser j is changed to pjbj

The price is the minimum bid the advertiser would need in

order to hold his current position.

The analysis of this version’s GSP is equal to normal GSP.

Ad Quality


The mysterious nature of ad quality.

How is ad quality computed?

Can estimate by actually observing the click through rate of the ad.

But search engines don’t tell the actual way.

How does the behavior of a matching market such as this one

change when the precise rules of the allocation procedure are

being kept secret?

A still topic for potential research.

Complex Queries and Interactions Among

Keywords


Example 1.

A company selling ski vacation package to Switzerland.

“Switzerland”, “Swiss vacations”, “Swiss hotels”, …

With a fixed budget, how should the company go about

dividing its budget across different keywords?

Still challenging problem

† is a current research working on this problem.

†Paat Rusmevichientong and David P. Williamson. An adaptive algorithm for selecting profitable keywords for search-based advertising services. In Proc. 7th ACM Conference on Electronic Commerce, pages 260–269, 2006.

Complex Queries and Interactions Among

Keywords


Example 2.

Some users query “Zurich ski vacation trip December”

No advertiser bids this key words.

Which ads should the search engine show?

Even if relevant advertisers can be identified, how much should

they be charged for a click?

Existing search engines get some agreements.

This is very interesting potential further research.

Technology

Sponsored Search Markets (from Networks, Crowds, and Markets: Reasoning About a Highly Connected World)