Chapter 15 Sponsored Search Markets from Networks, Crowds, and Markets: Reasoning About a
Highly Connected World
Junpei Kawamoto
Reading seminar
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.
Chapter 15 - Sponsored Search Markets 3
Overview
Chapter 15 - Sponsored Search Markets 4
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
Chapter 15 - Sponsored Search Markets 5
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
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.
Chapter 15 - Sponsored Search Markets 6
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
Chapter 15 - Sponsored Search Markets 7
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.
Advertising as a Matching Market
Chapter 15 - Sponsored Search Markets 8
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.
Advertising as a Matching Market
Chapter 15 - Sponsored Search Markets 9
Constructing a Matching Market
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.
Constructing a Matching Market
Advertising as a Matching Market
a
b
c
x
y
z
slots advertisers click through
rates
10
5
2
revenues
per click
3
2
1
Chapter 15 - Sponsored Search Markets 10
valuations
30, 15, 6
20, 10, 4
10, 5, 2
Advertisers’ valuations for the slots
Constructing a Matching Market
Advertising as a Matching Market
a
b
c
x
y
z
slots advertisers click through
rates
10
5
2
revenues
per click
3
2
1
Chapter 15 - Sponsored Search Markets 11
valuations
30, 15, 6
20, 10, 4
10, 5, 2
Advertisers’ valuations for the slots
the benefit advertiser j receives from an ad in slot i, vij = rivj
Constructing a Matching Market
Advertising as a Matching Market
a
b
c
x
y
z
slots advertisers click through
rates
10
5
2
revenues
per click
3
2
1
Chapter 15 - Sponsored Search Markets 12
valuations
30, 15, 6
20, 10, 4
10, 5, 2
Advertisers’ valuations for the slots
the benefit advertiser j receives from an ad in slot i, vij = rivj
Advertising as a Matching Market
Chapter 15 - Sponsored Search Markets 13
Constructing a Matching Market
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
Advertising as a Matching Market
Chapter 15 - Sponsored Search Markets 14
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
Advertising as a Matching Market
Chapter 15 - Sponsored Search Markets 15
Obtaining Market-Clearing Prices
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
Obtaining Market-Clearing Prices
Advertising as a Matching Market
a
b
c
x
y
z
slots advertisers click through
rates
10
5
2
revenues
per click
3
2
1
Chapter 15 - Sponsored Search Markets 16
valuations
30, 15, 6
20, 10, 4
10, 5, 2
the benefit advertiser j receives from an ad in slot i, vij = rivj
Finally obtained the perfect-seller graph.
Advertising as a Matching Market
Chapter 15 - Sponsored Search Markets 17
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
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 18
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?
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 19
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
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 20
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
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)
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 21
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
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.
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 22
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.
Vickrey-Clarke-Groves (VCG) principles
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 23
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
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 24
Applying the VCG Principles to Matching Markets
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
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 25
Applying the VCG Principles to Matching Markets
a
b
c
x
y
z
slots advertisers price valuations
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
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 26
Applying the VCG Principles to Matching Markets
a
b
c
x
y
z
slots advertisers price valuations
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
worth of 5. Harm = 5-2
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 27
Applying the VCG Principles to Matching Markets
a
b
c
x
y
z
slots advertisers price valuations
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
worth of 20. Harm = 20-10
z gets c, which is worthy of
2, instead of b, which is
worth of 5. Harm = 5-2
10+3 = 13
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 28
Applying the VCG Principles to Matching Markets
a
b
c
x
y
z
slots advertisers price valuations
30, 15, 6
20, 10, 4
10, 5, 2
For example
13
3
0
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 29
Applying the VCG Principles to Matching Markets
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.
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 30
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)
Encouraging Truthful Bidding
in Matching markets: The VCG Principle
Chapter 15 - Sponsored Search Markets 31
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:
Truth-Telling as a Dominant Strategy
Chapter 15 - Sponsored Search Markets 32
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.
Analyzing the VCG Procedure:
Truth-Telling as a Dominant Strategy
Chapter 15 - Sponsored Search Markets 33
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.
Analyzing the VCG Procedure:
Truth-Telling as a Dominant Strategy
Chapter 15 - Sponsored Search Markets 34
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.
We’ll focus the first part.
Analyzing the VCG Procedure:
Truth-Telling as a Dominant Strategy
Chapter 15 - Sponsored Search Markets 35
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
Analyzing the VCG Procedure:
Truth-Telling as a Dominant Strategy
Chapter 15 - Sponsored Search Markets 36
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)
Analyzing the VCG Procedure:
Truth-Telling as a Dominant Strategy
Chapter 15 - Sponsored Search Markets 37
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
Chapter 15 - Sponsored Search Markets 38
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
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 39
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.
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 40
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
revenues
per click
7
6
1
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 41
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
revenues
per click
7
6
1
price
10×6
4×1
0
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 42
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
revenues
per click
7
6
1
payoff price
60
4
0
70 - 60
24 - 4
10×7
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 43
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
revenues
per click
7
6
1
bid
5
6
1
x lies
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 44
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
revenues
per click
7
6
1
bid
5
6
1
Changed
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 45
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
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
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 46
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
revenues
per click
7
6
1
payoff price
4
50
0
28 - 4
24 - 4
bid
5
6
1
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 47
Truth-telling may not be an equilibrium.
a
b
c
x
y
z
slots advertisers click through
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.
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 48
Multiple and non-optimal equilibria.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
bid
5
4
2
bid
3
5
1
Both are Nash equilibrium.
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 49
Multiple and non-optimal equilibria.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
a
b
c
x
y
z
slots advertisers click through
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
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 50
Multiple and non-optimal equilibria.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
a
b
c
x
y
z
slots advertisers click through
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.
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 51
Multiple and non-optimal equilibria.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
a
b
c
x
y
z
slots advertisers click through
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.
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 52
Multiple and non-optimal equilibria.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
a
b
c
x
y
z
slots advertisers click through
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
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 53
Multiple and non-optimal equilibria.
a
b
c
x
y
z
slots advertisers click through
rates
10
4
0
a
b
c
x
y
z
slots advertisers click through
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 Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 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
slots advertisers click through
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
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 55
The Revenue of GSP and VCG
VCG for the same example
a
b
c
x
y
z
slots advertisers click through
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
The Generalized Second Price Auction
Chapter 15 - Sponsored Search Markets 56
The Revenue of GSP and VCG
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
Chapter 15 - Sponsored Search Markets 57
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
Equilibria of the Generalized Second Price
Auction
Chapter 15 - Sponsored Search Markets 58
GSP always has a Nash equilibrium
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
Equilibria of the Generalized Second Price
Auction
Chapter 15 - Sponsored Search Markets 59
GSP always has a Nash equilibrium
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)
Equilibria of the Generalized Second Price
Auction
Chapter 15 - Sponsored Search Markets 60
GSP always has a Nash equilibrium
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
Equilibria of the Generalized Second Price
Auction
Chapter 15 - Sponsored Search Markets 61
GSP always has a Nash equilibrium
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
Equilibria of the Generalized Second Price
Auction
Chapter 15 - Sponsored Search Markets 62
GSP always has a Nash equilibrium
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
Equilibria of the Generalized Second Price
Auction
Chapter 15 - Sponsored Search Markets 63
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
Equilibria of the Generalized Second Price
Auction
Chapter 15 - Sponsored Search Markets 64
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
Chapter 15 - Sponsored Search Markets 65
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
Chapter 15 - Sponsored Search Markets 66
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
Chapter 15 - Sponsored Search Markets 67
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
Chapter 15 - Sponsored Search Markets 68
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
Chapter 15 - Sponsored Search Markets 69
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.