#### Transcript Sponsored Search - California Institute of Technology

```Sponsored Search
Cory Pender
Sherwin Doroudi
Zoe Abrams
Ofer Mendelevitch
John A. Tomlin
Introduction
search page related to user’s keywords
 Pay per click
 Earn millions a day through these
auctions

– Auction type is important
Bids
 Query frequencies

QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
– Not controlled by advertisers or search engine
– Few queries w/ large volume, many with low
volume
 Pricing and ranking algorithm

Solution
 Focus on small subset of queries
– Predictable volumes in near future
– Constitute large amount of total volume

Bids
 Query frequencies

Pricing and ranking algorithm
– Generalized second price (GSP) auction
– Rankings according to (bid) x (quality score)
– Charged minimum price needed to maintain rank

Goal: take these parameters into account,
maximize revenue
Motivating example
Reserve price is 
Bidder
Bid for q1 Bid for q2 Budget
b1
C1 + 
C1
C1
b2
C1
0
C1
b3
C1 - 
C1 - 
2 C1
Allocation Shown
for q1
Greedy
b1
Shown
for q2
b3
Total
Revenue
C1 + 
Optimal
b1
2C1 - 
b2
Problem Definition
Queries Q = {q1, q2, q3, ..., qN}
 Bidders B = {b1, b2, b3, ..., bM}
 Bidding state A(t); Aij(t) is j’s bid
for i-th query
 dj is j’s daily budget
 vi is estimate of query frequency
 Li = {jp : jp  B, p = 1, ..., Pi}
 Lik = {jik : jik  Li, l ≤ Lik ≤ P}

Ranking and revenue






QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this
picture. and a
QuickTime™
Bid-ranking TIFF (LZW) decompressor
Revenue-ranking areQuickTi
neededme™
to see
andthis
a picture.
TIFF (LZW) decompressor
So, for slate k,
are needed to see this pi cture.
QuickTime™ and a
TIFF (LZW) decompressor
Price per click: are needed to see this picture.
Independent click through rates
Qu ickTime ™ a nd a
TIFF (L ZW) dec omp ress or
are nee ded to s ee th is p ictur e.
Revenue-per-search:
Total revenue:
Qui ckTime™ and a
TIFF ( LZW) decompressor
are needed to see this pi cture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Bidder’s cost

Total spend for j:
Quic kT ime™ and a
T IFF (LZW) dec ompres sor
are needed to s ee this pi cture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Linear program
Queries i = 1, ..., N
 Bidders j = 1, ..., M
 Slates k = 1, ..., Ki
 Data: dj, vi, cijk, rik
 Variables: xik
 Constraints:

– Budget:
– Inventory:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTi me™ and a
T IFF (LZW) decompressor
are needed to see thi s pi cture.
Objective function



Maximize revenue:
Value objective:
Clicks objective:
Quic kT ime™ and a
T IFF (LZW) dec ompres sor
are needed to s ee this pi cture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Column Generation
Each column represents a slate
 Could make all possible columns

– But for each query, exponential in number
of bidders
 j: Marginal value for j’s budget
 i: Marginal value for ith keyword
QuickTime™ and a
(LZW) decompressor
 Profit if areTIFF
needed to see this picture.
 Maximize

QuickTi me™ and a
TIFF (LZW) decom pressor
are needed to see this pi cture.
How to maximize?
If small number of bidders for a query,
enumerate all legal subsets Lik, find
maxima, see if adding increases profit
 Otherwise, use algorithm described in
another paper

ebay.com
tigerdirect.com
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
?
nextag.com
priceline.com
Summary (so far)






Various bidders vying for spots on the slate
for each query
Constrained by budget, query frequencies,
ranking method
Solve LP for some initial set of slates
slates
Re-solve LP, if necessary
Can be applied to maximize revenue or
efficiency
Simulation Methodology

Compare this method to greedy algorithm
– For greedy, assign what gets most revenue at the
time; when bidder’s budget is reached, take them
out of the pool

Used 5000 queries
 For 11 days, retrieved hourly data on bidders,
bids, budgets
 To determine which ads appear, assign based
on frequencies fik = xik/vi
 After each hour, see if anyone has exceeded
budget
Simulation Results
Current method better than greedy
method, when optimizing over revenue
or efficiency
 Larger gain for revenue when revenue
optimized
 Revenue and efficiency are closely tied

Gains when efficiency is maximized
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Gains when revenue is maximized
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Impact on bidders
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Limitations
Illegitimate price hikes for other bidders
if one person exceeds budget in middle
of hour
 Assumption that expected number of
clicks are correct
 For the purposes of the simulation,
expect these to affect greedy and LP
optimization similarly

Future work

Focus on less frequent queries
– Frequencies harder to predict
– Some work has been done (doesn’t incorporate
pricing and ranking)

Keywords with completely unknown
frequencies
 Parallel processing for submarkets
 Investigate how advertisers might respond to
this method
– Potential changes in reported bids/budgets
```