Hybrid Keyword Auctions

1. Hybrid Keyword Auctions Ashish Goel Stanford University Joint work with Kamesh Munagala, Duke University

2. 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

3. Cost-Per-Click Auction Auctioneer (Search Engine) Bid = Cost per Click Advertiser C

4. Cost-Per-Click Auction CTR estimate Auctioneer (Search Engine) Bid = Cost per Click Advertiser Q C

5. 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

6. 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

7. 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?

10. 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

11. Hybrid Scheme: 2-Dim Bid M = Cost per Impression C= Cost per Click Auctioneer (Search Engine) Advertiser <M,C >

12. Hybrid Scheme M = Cost per Impression C= Cost per Click CTR estimate Auctioneer (Search Engine) Advertiser Q <M,C >

13. 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 }

14. 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 > …

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. Key Point Implementing the properties need both per impression and per click bids

22. 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

23. 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

24. 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)

25. Bayesian Model for CTR True underlying CTR = p Auctioneer (Search Engine) Advertiser

26. Bayesian Model for CTR True underlying CTR = p Prior distribution Pauc Prior distribution Padv (Public) (Private) Auctioneer (Search Engine) Advertiser

27. 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

28. 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

29. 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

30. 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

31. 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)

32. Specific Class of Priors

33. Conjugate Beta Priors • Auctioneer’s Paucfor advertiseri =Beta(,) • ,are positive integers • Conjugate of Bernoulli distribution (CTR) • Expected value =/ ( + )

34. 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(,)

35. 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

36. 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

37. Benefits to Auctioneer and Advertisers

38. 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

39. 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

40. 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

41. 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

42. Flexibility for Advertisers AssumeC = 1 Per-impression bid M = p Advertiser Knows p Q =  / ( + ) Auctioneer (Search Engine) Pauc = Beta(,)

43. 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

44. 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

45. 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

46. 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

47. Dynamic Properties

48. 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?

49. 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!

50. 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