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Hybrid Keyword Auctions. Ashish Goel Stanford University Joint work with Kamesh Munagala, Duke University. Online Advertising. Pricing Models CPM (Cost per thousand impressions) CPC (Cost per click) CPA (Cost per acquisition) Conversion rates:

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hybrid keyword auctions

Hybrid Keyword Auctions

Ashish Goel

Stanford University

Joint work with Kamesh Munagala, Duke University

online advertising
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
cost per click auction
Cost-Per-Click Auction

Auctioneer

(Search Engine)

Bid = Cost per Click

Advertiser

C

cost per click auction4
Cost-Per-Click Auction

CTR estimate

Auctioneer

(Search Engine)

Bid = Cost per Click

Advertiser

Q

C

cost per click auction5
Cost-Per-Click Auction

CTR estimate

Auctioneer

(Search Engine)

Bid = Cost per Click

Advertiser

Q

C

  • Value/impression ordering: C1Q1 > C2Q2 > …
  • Give impression to bidder 1 at CPC = C2Q2/Q1
cost per click auction6
Cost-Per-Click Auction

CTR estimate

Auctioneer

(Search Engine)

Bid = Cost per Click

Advertiser

Q

C

  • Value/impression ordering: C1Q1 > C2Q2 > …
  • Give impression to bidder 1 at CPC = C2Q2/Q1
  • VCG Mechanism: Truthful for a single slot, assuming static CTR estimates
    • Can be made truthful for multiple slots [Vickrey-Clark-Groves, Myerson81, AGM06]
    • This talk will focus on single slot for proofs/examples
when does this work well
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?
possible solutions
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
hybrid scheme 2 dim bid
Hybrid Scheme: 2-Dim Bid

M = Cost per Impression

C= Cost per Click

Auctioneer

(Search Engine)

Advertiser

<M,C >

hybrid scheme
Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

hybrid scheme13
Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

  • Advertiser’s score Ri = max { Mi , Ci Qi }
hybrid scheme14
Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

  • Advertiser’s score Ri = max { Mi , Ci Qi }
  • Order by score: R1 > R2 > …
hybrid scheme15
Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

  • Advertiser’s score Ri = max { Mi , Ci Qi }
  • Order by score: R1 > R2 > …
  • Give impression to bidder 1:
    • If M1 > C1Q1then chargeR2per impression
    • If M1 < C1Q1then chargeR2 / Q1per click
example cpc auction
Example: CPC Auction

Bidder 1

Bidder 2

Per click cost C

5

10

Conversion rate

estimate Q

0.1

0.08

0.5

0.8

C * Q

CPC auction allocates to bidder 2 at CPC = 0.5/0.08 = 6.25

example hybrid auction
Example: Hybrid Auction

Bidder 1

Bidder 2

Per click cost C

5

10

Conversion rate

estimate Q

0.1

0.08

0.5

0.8

C * Q

Per impression

cost M

0

1.0

Max {M, C * Q}

1.0

0.8

Hybrid auction allocates to bidder 1 at CPI = 0.8

why such a model
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 such a model19
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
provable benefits
Provable Benefits
  • Search engine:Better monetization of low volume keywords
      • Typical case: Unbounded gain over CPC auction
      • Pathological worst case: Bounded loss over CPC auction
  • Advertiser: Opportunity to make the search engine converge to the correct CTR estimate without paying a premium
  • Technical:
    • Truthful
    • Accounts for risk characteristics of the advertiser
    • Allows users to implement complex strategies
key point
Key Point

Implementing the properties need both

per impression and per click bids

multiple slots
Multiple Slots
  • Show the top K scoring advertisers
      • Assume R1 > R2 > … > RK > RK+1…
  • Generalized Second Price (GSP) mechanism:
      • For the ith advertiser, if:
        • IfMi > QiCithen charge Ri+1per impression
        • IfMi < QiCithen charge Ri+1 / Qi per click
multiple slots23
Multiple Slots
  • Show the top K scoring advertisers
      • Assume R1 > R2 > … > RK > RK+1…
  • Generalized Second Price (GSP) mechanism:
      • For the ith advertiser, if:
        • IfMi > QiCithen charge Ri+1per impression
        • IfMi < QiCithen charge Ri+1 / Qi per click
  • Can also implement VCG [Vickrey-Clark-Groves, Myerson81, AGM06]
      • Need separable CTR assumption
      • Details in the paper
uncertainty model for ctr
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)
bayesian model for ctr
Bayesian Model for CTR

True underlying CTR = p

Auctioneer

(Search Engine)

Advertiser

bayesian model for ctr26
Bayesian Model for CTR

True underlying CTR = p

Prior distribution Pauc

Prior distribution Padv

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

bayesian model for ctr27
Bayesian Model for CTR

True underlying CTR = p

Per-impression bid

M

CTR estimate

Q

Prior distribution Pauc

Prior distribution Padv

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

bayesian model for ctr28
Bayesian Model for CTR

True underlying CTR = p

Per-impression bid

M

CTR estimate

Q

Prior distribution Pauc

Prior distribution Padv

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

Each agent optimizes based on its current “belief” or prior:

Beliefs updated with every impression

Over time, become sharply concentrated around true CTR

what is a prior
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 CTRp
  • Priors are only for purpose of analysis
    • Mechanism is well-defined regardless of modeling assumptions
truthfulness
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
truthfulness31
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 andtrue CTR p

Elicits advertiser’s “expected belief” about the CTR!

Holds in many other settings (more later)

conjugate beta priors
Conjugate Beta Priors
  • Auctioneer’s Paucfor advertiseri =Beta(,)
      • ,are positive integers
      • Conjugate of Bernoulli distribution (CTR)
      • Expected value =/ ( + )
conjugate beta priors34
Conjugate Beta Priors
  • Auctioneer’s Paucfor advertiseri =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(,)
evolution of beta priors
Evolution of Beta Priors

Denotes Beta(1,1)

Uniform prior

Uninformative

Click

1,1

No Click

1/2

1/2

2,1

1,2

2/3

1/3

1/3

2/3

E[Pauc]= 1/4

3,1

2,2

1,3

1/4

1/2

3/4

1/2

3/4

1/4

4,1

3,2

2,3

1,4

E[Pauc]= 2/5

properties of beta priors
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
advertiser certain of ctr
Advertiser Certain of CTR

True underlying CTR = p

Per-impression bid

M = Cp

CTR estimate

Q =  / ( + )

Pauc = Beta(,)

Knows p

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

properties of auction
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 Paucconverge to p without paying premium
      • But pays huge premium for achieving this in CPC auction
better monetization
Better Monetization

p1

Adv. 1

Q ≈ 1 / log n

Pauc = Beta (, log n)

p2

Adv. 2

Auctioneer

p3

Adv. 3

Pauc = Beta (, log n)

  • Low volume keyword:
  • Auctioneer’s prior has high variance
  • Some pi close to 1 with high probability

pn

Adv. n

better monetization41
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
flexibility for advertisers
Flexibility for Advertisers

AssumeC = 1

Per-impression bid

M = p

Advertiser

Knows p

Q =  / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

flexibility for advertisers43
Flexibility for Advertisers

Per-impression bid

M = p

Advertiser

Knows p

Q =  / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

Wins on per impression bid

Pays at most p per impression

flexibility for advertisers44
Flexibility for Advertisers

T impressions

N clicks

Per-impression bid

M = p

Advertiser

Knows p

Makes Q converge to p

Q =  / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

Wins on per impression bid

Pays at most p per impression

flexibility for advertisers45
Flexibility for Advertisers

T impressions

N clicks

Per-impression bid

M = p

Advertiser

Knows p

Makes Q converge to p

Q =  / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

Now switch to CPC bidding

flexibility for advertisers46
Flexibility for Advertisers
  • If Q converges in T impressions resulting in N clicks:
    • ( N  T) ≥ 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
uncertain advertisers
Uncertain Advertisers
  • Advertiser “wishes” CTR p toresolve 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?
uncertain advertisers49
Uncertain Advertisers
  • Advertiser “wishes” CTR p toresolve 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!
the issue with dynamics
The Issue with Dynamics

Padv1

Adv. 1

Pauc1

Auctioneer

Pauc2

Padv2

Adv. 2

[Bapna & Weber ‘05, Athey & Segal ‘06]

  • 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
semi myopic advertiser
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!

semi myopic advertiser52
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
summary
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]
conclulsion and open questions
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
open questions
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?
open questions56
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]
truthfulness57
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 score

If max(Cy, C Q) <R2then Price = 0

Else:

If y < Q then: Price = x R2 / Q

If y > Q then: Price = R2