Discrete Choice Model of Bidder Behavior in Sponsored Search

1. Discrete Choice Model of Bidder Behavior in Sponsored Search Quang Duong qduong@umich.edu University of Michigan SebastienLahaie lahaies@yahoo-inc.com Yahoo! Research, NY

2. What are Sponsored Search Auctions?

3. Problem • Given: auction data (bids, ranks, prices, click-through rates) • Objective (of the search engine): • Predict auction outcomes: ranks, realized clicks • Discover bidders’ values

4. Challenges • Some bidders/advertisers keep their bids mostly static • Some actively manage their bids [over the course of 4 weeks]

5. Related Work • Revealed preference from bid updates (ineffective with inactive bidders) [Borgers et al. ‘08] • Distributions over opponents’ bids (assuming that bidders’ values change with each bid update). [Athey and Nekipelov ‘10, Pin and Key ‘11]

6. Key Observation • Advertisers’ ranks (of active and inactive bidders) vary considerably, due to: • Variation in click-through rate • Variation in the number of competitors and the reserve score/price • Variation in others’ bids

7. Approach Model how an advertiser chooses ranks, instead of bids: using discrete choice models Use the discrete choice model of ranks to predict other auction outcomes and discover values.

8. Sponsored Search Overview • N agents (advertisers/bidders) bid for K slots • Agent i: • bids bi • has value per click vi for its ad • is assigned weight wi (past click through rate = quality/clickability of ads by i)

9. Generalized Second-Price Auction in Sponsored Search • Ranking (descending order) is based on: wibi • (Second) Price that the i-th advertiser pays: price per click pi = wi+1bi+1 / wi

10. Advertiser Utility • Click through rate (CTR): wixj • advertiser effect wi • position effect xj: different ranks induce different rates • Advertiser i’s utility = value – cost Vij = (vi – pj)wixj • Fix agent i, and care about relative utility Vj = (v – pj)xj

11. Discrete Choice: Overview • From the modeler’s perspective: • The agent maximizes some unknown utility: Uj= Vj+ ej, instead of the actual Vj • Error term ejaccounts for changes in the agent’s choice of ranks, even when bids are held fixed

12. Discrete Choice: Error Term • The distribution of an agent’s error/regret from leaving its bid unchanged is induced by exogenous changes: • updates to the advertiser effects (clickability) • the number of opponents, and the reserve price. • other advertisers’ bids

13. Discrete Choice: Logit Model • Assumption: error ej~ logistic distribution • The probability of choosing rank j follows a discrete choice model incorporating uncertainty (ej) in utility Pr(j) = exp(λVj) / Σkexp(λVk) whereλreflects a bidder’s “rationality”: λ= inverse error (ej) variance

14. Discrete Choice: Summary • Random utility Uj = Vj + ej • Error term ~ logistic distribution • The rank probability is given by a logit function • The modeler maximizes the likelihood of rank data: • Given estimated prices, position effects  learn v and λ

15. Data Description • Yahoo’s sponsored search logs for July, 2010. • We randomly sampled 20 keywords from each of the top 5 keyword deciles by volume. • Training: first 3 weeks, and test: last week • Data filtering • Final data set: 197 advertisers

16. Observations • Some advertisers rarely vary their bids (top left) • Substantial rank variation (bottom left)

17. Baseline Models • Constant rank model (rank prediction only) • Historical click model (click prediction only) • Stochastic model [Pin and Key, ‘11]: specifies each agent as a pair of ad and bid value, and estimates: • Empirical distribution of bids • Empirical distribution of number of bidders

18. Learned Parameters (Left) Value estimates > average bids (with no constraints on the logit model) (Right) Low bidders: low regret, little variance <> high bidders

19. Rank Predictions • Logit > Constant Rank and Stochastic • Prediction performances improve as volume increases

20. Realized Click Predictions • Historical Click (Constant Model) best predicts clicks for least clicked ads • Logit best predicts clicks for more clicked ads • Note: stochastic model has to use actual bids to predict clicks

21. Conclusions • Introduce a discrete-choice approach to modeling bidding behavior of both active and inactive bidders in sponsored search auctions • Generate bidder value estimates that are consistent with theory • Empirically show that the logit model predicts ranks and clickswell

22. Future Work • Add position-specific intercepts to the utility specification (“branding effect” of slots) • Use a nested logit model to accommodate the variation in the number of bidders • Scale up our empirical analysis and include more high-click rather than high-volume ads

23. Thank You! qduong@umich.edu www.eecs.umich.edu/~qduong