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```					Sponsored Search

Cory Pender
Sherwin Doroudi
Optimal Delivery of Sponsored Search

Zoe Abrams
Ofer Mendelevitch
John A. Tomlin
Introduction

 Search engines (Google, Yahoo!, MSN)
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
– Not controlled by advertisers or search engine
TIFF (LZW) decompressor
decompressor
are needed to see this picture.

– 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
– Controlled by advertisers
   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       Shown     Total
for q1      for q2    Revenue
Greedy     b1          b3        C1 + 
Optimal      b2        b1        2C1 - 
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
   Bid-ranking -            TIFF (LZW) decompressor
are needed to see this picture. and a
QuickTime™
   Revenue-ranking -                       TIFF (LZW) decompressor
needed to see this
areQuickTime™ and a picture.
TIFF (LZW) decompressor
   So, for slate k,               are needed to see this picture.
QuickTime™ and a
   Price per click: are needed to see this picture.
TIFF (LZW) decompressor

   Independent click through rates                                                    Q uic kT im e™ an d a
T IFF ( LZ W) d ec o mp r es s or
a re n ee d ed to s e e th is p ictu r e.

QuickTime™ an d a
   Revenue-per-search:                                           TIFF (LZW) decompressor
are need ed to see this p icture .

Total revenue:
Qui ckTi me™ and a
TIFF (LZW) decompresso r
are ne ede d to see thi s pi cture.
Bidder’s cost
Quic kTime™ and a

   Total spend for j:               TIFF (LZW) dec ompressor
are needed to s ee this pic ture.

QuickTime™ and a
TIFF (LZW) decompressor
are neede d 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:
QuickTime™ and a
– Budget:          TIFF (LZW) decompressor
are needed to see this picture.

QuickTime™ and a
– Inventory:      TIFF (LZW) decompress or
are needed to see this picture.
Objective function
Quic kTime™ and a

   Maximize revenue:          TIFF (LZW) dec ompress or
are needed to s ee this picture.

QuickTime™ and a
TIFF (LZW) decompressor
   Value objective:       are needed to see this picture.

QuickTime™ and a
TIFF (LZW) decompressor
   Clicks objective:   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
 Start with some initial set of columns
 j: Marginal value for j’s budget
 i: Marginal value for ith keyword
QuickTime™ and a
 Profit if areTIFF (LZW) see this picture.
needed to
decompressor

QuickTime™ and a

 Maximize
TIFF (LZW) decompressor
are needed to see this picture.
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
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
ebay.com                 Qui ckTi me™ and a
nextag.com
TIFF (LZW) decomp re ssor
are ne ede d to see thi s pi cture.

tigerdirect.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
   Check if profit can be made by adding new
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™ an d a
TIFF (LZW) decomp resso r
are need ed to see this picture .
Gains when revenue is maximized

QuickTime™ an d a
TIFF (LZW) decomp ressor
are need ed to see this p icture .
Impact on bidders

QuickTime™ and a
TIFF (LZW) decompressor
are neede d 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

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