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Hybrid Keyword Auctions

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

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  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?

  8. 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

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

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

  11. 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 }

  12. 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 > …

  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 } • Order by score: R1 > R2 > … • Give impression to bidder 1: • If M1 > C1Q1then chargeR2per impression • If M1 < C1Q1then chargeR2 / Q1per click

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

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

  20. 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

  21. 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

  22. 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)

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

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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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)

  30. Specific Class of Priors

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

  32. 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(,)

  33. 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

  34. 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

  35. Benefits to Auctioneer and Advertisers

  36. 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

  37. 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

  38. 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

  39. 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

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

  41. 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

  42. 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

  43. 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

  44. 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

  45. Dynamic Properties

  46. 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?

  47. 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!

  48. 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

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