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Hybrid Keyword Auctions
Ashish Goel
Stanford University
Joint work with Kamesh Munagala, Duke University
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Online Advertising
Pricing Models CPM (Cost per thousand impressions) CPC (Cost per click) CPA (Cost per acquisition) Conversion rates:
• Click-through-rate (CTR), conversion from clicks to acquisitions, …
Differences between these pricing models: Uncertainty in conversion rates:
• Sparse data, changing rates, … Stochastic fluctuations:
• Even if the conversion rates were known exactly, the number of clicks/conversions would still vary, especially for small samples
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Cost-Per-Click Auction
Advertiser Auctioneer(Search Engine)
Bid = Cost per Click
C
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Cost-Per-Click Auction
Advertiser Auctioneer(Search Engine)
Bid = Cost per Click
C
CTR estimate
Q
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Cost-Per-Click Auction
Advertiser Auctioneer(Search Engine)
Bid = Cost per Click
C
CTR estimate
Q
• Value/impression ordering: C1Q1 > C2Q2 > …
• Give impression to bidder 1 at CPC = C2Q2/Q1
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Cost-Per-Click Auction
Advertiser Auctioneer(Search Engine)
Bid = Cost per Click
C
CTR estimate
Q
VCG Mechanism: Truthful for a single slot, assuming static CTR estimatesCan be made truthful for multiple slots [Vickrey-Clark-Groves, Myerson81, AGM06]This talk will focus on single slot for proofs/examples
• Value/impression ordering: C1Q1 > C2Q2 > …
• Give impression to bidder 1 at CPC = C2Q2/Q1
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When Does this Work Well?
High volume targets (keywords) Good estimates of CTR
What fraction of searches are to high volume targets? Folklore: a small fraction
Motivating problem:
How to better monetize the low volume keywords?
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Possible Solutions
Coarse ad groups to predict CTR: Use performance of advertiser on possibly unrelated keywords
Predictive models Regression analysis/feature extraction
Taxonomies/clustering
Collaborative filtering
Learn the human brain!
Our approach: Richer pricing models + Learning
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Hybrid Scheme: 2-Dim Bid
Advertiser Auctioneer(Search Engine)
M = Cost per ImpressionC = Cost per Click
<M,C >
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Hybrid Scheme
Advertiser Auctioneer(Search Engine)
M = Cost per ImpressionC = Cost per Click
<M,C >
CTR estimate
Q
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Hybrid Scheme
Advertiser Auctioneer(Search Engine)
M = Cost per ImpressionC = Cost per Click
<M,C >
CTR estimate
Q
• Advertiser’s score Ri = max { Mi , Ci Qi }
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Hybrid Scheme
Advertiser Auctioneer(Search Engine)
M = Cost per ImpressionC = Cost per Click
<M,C >
CTR estimate
Q
• Advertiser’s score Ri = max { Mi , Ci Qi }
• Order by score: R1 > R2 > …
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Hybrid Scheme
Advertiser Auctioneer(Search Engine)
M = Cost per ImpressionC = Cost per Click
<M,C >
CTR estimate
Q
• Advertiser’s score Ri = max { Mi , Ci Qi }
• Order by score: R1 > R2 > …
• Give impression to bidder 1:
• If M1 > C1Q1 then charge R2 per impression• If M1 < C1Q1 then charge R2 / Q1 per click
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Example: CPC Auction
Bidder 1 Bidder 2
Per click cost C 5 10
Conversion rate estimate Q
0.1 0.08
C * Q 0.5 0.8
CPC auction allocates to bidder 2 at CPC = 0.5/0.08 = 6.25
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Example: Hybrid Auction
Bidder 1 Bidder 2
Per click cost C 5 10
Conversion rate estimate Q
0.1 0.08
C * Q 0.5 0.8
Hybrid auction allocates to bidder 1 at CPI = 0.8
Per impression cost M 1.0 0
Max {M, C * Q}
1.0 0.8
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Why Such a Model?
Per-impression bid: Advertiser’s estimate or “belief” of CTR
May or may not be an accurate reflection of the truth
Backward compatible with cost-per-click (CPC) bidding
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Why Such a Model?
Per-impression bid: Advertiser’s estimate or “belief” of CTR May or may not be an accurate reflection of the truth Backward compatible with cost-per-click (CPC) bidding
Why would the advertiser know any better? Advertiser aggregates data from various publishers Has domain specific models not available to auctioneer Is willing to pay a premium for internal experiments
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Provable Benefits
1. Search engine: Better monetization of low volume keywordsn Typical case: Unbounded gain over CPC auctionn Pathological worst case: Bounded loss over CPC auction
2. Advertiser: Opportunity to make the search engine converge to the correct CTR estimate without paying a premium
3. Technical:
a) Truthful
b) Accounts for risk characteristics of the advertiser
c) Allows users to implement complex strategies
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Key Point
Implementing the properties need both per impression and per click bids
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Multiple Slots
Show the top K scoring advertisers Assume R1 > R2 > … > RK > RK+1…
Generalized Second Price (GSP) mechanism: For the ith advertiser, if:
• If Mi > QiCi then charge Ri+1 per impression
• If Mi < QiCi then charge Ri+1 / Qi per click
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Multiple Slots
Show the top K scoring advertisers Assume R1 > R2 > … > RK > RK+1…
Generalized Second Price (GSP) mechanism: For the ith advertiser, if:
• If Mi > QiCi then charge Ri+1 per impression
• If Mi < QiCi then charge Ri+1 / Qi per click
Can also implement VCG [Vickrey-Clark-Groves, Myerson81, AGM06] Need separable CTR assumption Details in the paper
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Uncertainty Model for CTR
For analyzing advantages of Hybrid, we need to model: Available information about CTR
Asymmetry in information between advertiser and auctioneer
Evolution of this information over time
We will use Bayesian model of information Prior distributions
Specifically, Beta priors (more later)
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Bayesian Model for CTR
AdvertiserAuctioneer
(Search Engine)
True underlying CTR = p
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Bayesian Model for CTR
AdvertiserAuctioneer
(Search Engine)
True underlying CTR = p
Prior d
istr
ibut
ion
P adv
Prior distribution Pauc
(Priv
ate)
(Public)
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Bayesian Model for CTR
AdvertiserAuctioneer
(Search Engine)
CTR estimate Q
True underlying CTR = p
Prior d
istr
ibut
ion
P adv
Prior distribution Pauc
Per-impression bid M
(Priv
ate)
(Public)
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Bayesian Model for CTR
AdvertiserAuctioneer
(Search Engine)
CTR estimate Q
True underlying CTR = p
Prior d
istr
ibut
ion
P adv
Prior distribution Pauc
Per-impression bid M
Each agent optimizes based on its current “belief” or prior:
Beliefs updated with every impression
Over time, become sharply concentrated around true CTR
(Priv
ate)
(Public)
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What is a Prior?
Simply models asymmetric information Sharper prior More certain about true CTR p E[ Prior ] need not be equal to p
Main advantage of per-impression bids is when: Advertiser’s prior is “more resolved” than auctioneer’s Limiting case: Advertiser certain about CTR p
Priors are only for purpose of analysis Mechanism is well-defined regardless of modeling assumptions
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Truthfulness
Advertiser assumes CTR follows distribution Padv
Wishes to maximize expected profit at current step E[Padv] = x = Expected belief about CTR
Click utility = C
Expected profit = C x - Expected price
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Truthfulness
Advertiser assumes CTR follows distribution Padv
Wishes to maximize expected profit at current step E[Padv] = x = Expected belief about CTR
Click utility = C
Expected profit = C x - Expected price
Bidding (Cx, C) is the dominant strategy
Regardless of Q used by auctioneer and true CTR p
Elicits advertiser’s “expected belief” about the CTR!
Holds in many other settings (more later)
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Specific Class of Priors
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Conjugate Beta Priors
Auctioneer’s Pauc for advertiser i = Beta( , ) , are positive integers
Conjugate of Bernoulli distribution (CTR)
Expected value = / ( + )
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Conjugate Beta Priors
Auctioneer’s Pauc for advertiser i = Beta( , ) , are positive integers
Conjugate of Bernoulli distribution (CTR)
Expected value = / ( + )
Bayesian update with each impression: Probability of click = / ( + )
If click, new Pauc (posterior) = Beta( , )
If no click, new Pauc (posterior) = Beta( , )
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Evolution of Beta Priors
1,1
2,1 1,2
2,23,1 1,3
3,2 2,3 1,44,1
1/2 1/2
2/3 1/3 1/3 2/3
3/4 1/4
1/21/21/43/4
Denotes Beta(1,1)Uniform priorUninformative
E[Pauc] = 1/4
E[Pauc] = 2/5
Click
No Click
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Properties of Beta Priors
Larger , Sharper concentration around p
Uninformative prior: Beta(,) = Uniform[0,1]
Q = E[Pauc] = / ( + )
Auctioneer’s expected “belief” about CTR
Could be different from true CTR p
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Benefits to Auctioneer and Advertisers
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Advertiser Certain of CTR
AdvertiserAuctioneer
(Search Engine)
CTR estimate Q = / ( + )
True underlying CTR = p
Knows p
Pauc = Beta(,)
Per-impression bid M = Cp
(Priv
ate)
(Public)
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Properties of Auction
Revenue properties for auctioneer: Typical case benefit: log n times better than CPC scheme
Bounded pathological case loss: 36% of CPC scheme
Unbounded gain versus bounded loss!
Flexibility for advertiser: Can make Pauc converge to p without paying premium
But pays huge premium for achieving this in CPC auction
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Better Monetization
Adv. 1
Adv. 2
Adv. 3
Adv. n
…
Auctioneer
p1
p2
p3
pn
Pauc = Beta (, log n)
P auc = Beta (, log n)
Q ≈ 1 / log n
Low volume keyword:
• Auctioneer’s prior has high variance
• Some pi close to 1 with high probability
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Better Monetization
Hybrid auction: Per-impression bid elicits high pi
CPC auction allocates slot to a random advertiser
Theorem: Hybrid auction generates log n times
more revenue for auctioneer than CPC auction
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Flexibility for Advertisers
Advertiser
Auctioneer(Search Engine)
Q = / ( + )
Knows p
Pauc = Beta(,)
Per-impression bid M = p
Assume C = 1
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Flexibility for Advertisers
Advertiser
Auctioneer(Search Engine)
Q = / ( + )
Knows p
Pauc = Beta(,)
Per-impression bid M = p
Wins on per impression bid
Pays at most p per impression
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Flexibility for Advertisers
Advertiser
Auctioneer(Search Engine)
Q = / ( + )
Knows p
Pauc = Beta(,)
Per-impression bid M = p
T impressionsN clicks
Makes Q converge to
p
Wins on per impression bid
Pays at most p per impression
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Flexibility for Advertisers
Advertiser
Auctioneer(Search Engine)
Q = / ( + )
Knows p
Pauc = Beta(,)
Per-impression bid M = p
T impressionsN clicks
Makes Q converge to
p
Now switch to CPC bidding
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Flexibility for Advertisers
If Q converges in T impressions resulting in N clicks: ( NT) ≥ p
Since Q = /( + ) < p, this implies N ≥ T p
Value gain = N; Payment for T impressions at most T * p
No loss in utility to advertiser!
In the existing CPC auction: The advertiser would have to pay a huge premium for getting
impressions and making the CTR converge
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Dynamic Properties
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Uncertain Advertisers
Advertiser “wishes” CTR p to resolve to a high value In that case, she can gain utility in the long run
… but CTR resolves only on obtaining impressions!
Should pay premium now for possible future benefit What should her dynamic bidding strategy be?
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Uncertain Advertisers
Advertiser “wishes” CTR p to resolve to a high value In that case, she can gain utility in the long run … but CTR resolves only on obtaining impressions!
Should pay premium now for possible future benefit What should her dynamic bidding strategy be?
Key contribution: Defining a new Bayesian model for repeated auctions Dominant strategy exists!
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The Issue with Dynamics
Adv. 1
Adv. 2
Auctioneer
Padv1
Padv2
Pauc1
Pauc2
Advertiser 1 underbids so that:• Advertiser 2 can obtain impressions• Advertiser 2 may resolve its CTR to a low value• Advertiser 1 can then obtain impressions cheaply
[Bapna & Weber ‘05, Athey & Segal ‘06]
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Semi-Myopic Advertiser Maximizes utility in contiguous time when she wins the auction
Priors of other advertisers stay the same during this time Once she stops getting impressions, cannot predict future
… since future will depend on private information of other bidders!
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Semi-Myopic Advertiser Maximizes utility in contiguous time when she wins the auction
Priors of other advertisers stay the same during this time Once she stops getting impressions, cannot predict future
… since future will depend on private information of other bidders!
Advertiser always has a dominant hybrid strategy Bidding Index: Computation similar to the Gittins index
Advertiser can optimize her utility by dynamic programming
Socially optimal in many reasonable scenarios Implementation needs both per-impression and per-click bids
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Summary
Allow both per-impression and per-click bids Same ideas work for CPM/CPC + CPA
Significantly higher revenue for auctioneer
Easy to implement Hybrid advertisers can co-exist with pure per-click advertisers
Easy path to deployment/testing
Many variants possible with common structure: Optional hybrid bids
Impression + Click [S. Goel, Lahaie, Vassilvitskii, 2010]
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Conclulsion and Open Questions
Learning is important in Online advertising Remember that there are multiple strategic participants
Design richer pricing and communication signals
Some issues that need to be addressed: Whitewashing: Re-entering when CTR is lower than the default
Fake Clicks: Bid per impression initially and generate false
clicks to drive up CTR estimate Q Switch to per click bidding when slot is “locked in” by the high Q
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Open Questions
Some issues that need to be addressed: Whitewashing: Re-entering when CTR is lower than the default Fake Clicks: Bid per impression initially and generate false
clicks to drive up CTR estimate Q Switch to per click bidding when slot is “locked in” by the high Q
Analysis of semi-myopic model Other applications of separate beliefs?
![Page 56: Hybrid Keyword Auctions Ashish Goel Stanford University Joint work with Kamesh Munagala, Duke University](https://reader033.vdocument.in/reader033/viewer/2022061306/5514765f550346494e8b6308/html5/thumbnails/56.jpg)
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Open Questions
Some issues that need to be addressed: Whitewashing: Re-entering when CTR is lower than the default Fake Clicks: Bid per impression initially and generate false
clicks to drive up CTR estimate Q Switch to per click bidding when slot is “locked in” by the high Q
Analysis of semi-myopic model Other applications of separate beliefs?
Connections of Bayesian mechanisms to: Regret bounds and learning [Nazerzadeh, Saberi, Vohra ‘08]
Best-response dynamics [Edelman, Ostrovsky, Schwarz ‘05]
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Truthfulness
Advertiser assumes CTR follows distribution Padv
Wishes to maximize expected profit at current step E[Padv] = x = Expected belief about CTR
Utility from click = C
Expected profit = C x - Expected price
Let Cy = Per impression bid R2 = Highest other scoreIf max(Cy, C Q) < R2 then Price = 0Else:
If y < Q then: Price = x R2 / Q
If y > Q then: Price = R2