# Discrete Choice Model of Bidder Behavior in Sponsored Search Quang Duong University of Michigan Sebastien Lahaie

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

What are Sponsored Search Auctions? 2

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

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

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] 5

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 6

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. 7

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

Generalized Second-Price Auction in Sponsored Search Ranking (descending order) is based on: w i b i (Second) Price that the i-th advertiser pays: price per click p i = w i+1 b i+1 / w i 9

Advertiser Utility Click through rate (CTR): w i x j – advertiser effect w i – position effect x j : different ranks induce different rates Advertiser i’s utility = value – cost V ij = (v i – p j )w i x j Fix agent i, and care about relative utility V j = (v – p j )x j 10

Discrete Choice: Overview From the modeler’s perspective: – The agent maximizes some unknown utility: U j = V j + e j, instead of the actual V j – Error term e j accounts for changes in the agent’s choice of ranks, even when bids are held fixed 11

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 12

Discrete Choice: Logit Model Assumption: error e j ~ logistic distribution The probability of choosing rank j follows a discrete choice model incorporating uncertainty (e j ) in utility Pr(j) = exp(λV j ) / Σ k exp(λV k ) where λ reflects a bidder’s “rationality”: λ = inverse error (e j ) variance 13

Discrete Choice: Random Utility We rewrite the random utility U j function U j = β v x j + β p x j p j + e j to obtain λ = β p -2 /C where: -β p : marginal utility of money (-β v / β p ) = v: agent’s estimated value for ads 14

Discrete Choice: Summary Random utility U j = V j + e j 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 clicks well 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 24

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