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Laddered auction

Laddered auction. Ashish Goel. tanford University. http://www.stanford.edu/~ashishg. Based on slides by Gagan Aggarwal. Setting. Different slots provide different amounts of visibility. Problem: How to match advertisers to slots. What price to charge. Large, dynamic markets.

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Laddered auction

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  1. Laddered auction AshishGoel tanford University http://www.stanford.edu/~ashishg Based on slides by Gagan Aggarwal

  2. Ashish Goel (ashishg@stanford.edu)

  3. Setting • Different slots provide different amounts of visibility. • Problem: • How to match advertisers to slots. • What price to charge. • Large, dynamic markets. • Current solution: run an auction. Ashish Goel (ashishg@stanford.edu)

  4. Next-price auctionA.k.a. Generalized Second-Price auction • Advertisers submit bids. • Place advertisers in decreasing order of weighted bid. • Yahoo uses (used?) uniform weights. • Google weights each advertiser by her quality score. • Each advertiser is charged the bid of next-lower advertiser (scaled appropriately in the weighted case). Ashish Goel (ashishg@stanford.edu)

  5. Example 30 2nd slot 20 3rd slot Top slot Bid/click 14 2nd slot 10 3rd slot 4th slot 0 15 20 30 50 Clicks/100 impressions Ashish Goel (ashishg@stanford.edu)

  6. What does an advertiser want? • An advertiser pays only when her ad gets clicked. • Valuation = True worth of a click. • E.g. the expected value of a sale generated by the click. • Profit = valuation – price. • CTR = fraction of times an ad gets clicked = # clicks / # impressions. Ashish Goel (ashishg@stanford.edu)

  7. Auction is not truthful • An auction is truthful if the best strategy for a bidder is to bid her true valuation. • Current ad auctions are not truthful • Top slots are priced higher than bottom slots. • Increase in CTR may not always compensate for the higher price • Assumptions: • Infinite budget per advertiser. • Rational advertisers who are trying to maximize profit, defined as Profit = valuation - price Ashish Goel (ashishg@stanford.edu)

  8. Example 30 2nd slot 20 3rd slot 14 Bid/Valuation per click 10 0 15 20 30 50 Clicks/100 impressions Ashish Goel (ashishg@stanford.edu)

  9. Ashish Goel (ashishg@stanford.edu)

  10. CTR separates into a position-specific factor and an advertiser-specific factor. Why a new auction? • A good bid depends on others’ bids. • Competing bids keep changing due to bid changes by others and due to budget smoothing. • Not-so-savvy advertisers are unable to keep up and often bid suboptimally. • Some use third parties to do their bidding. • Goal: Simplify the task of bidding by making the auction truthful (the best strategy for a bidder is to bid its true valuation). • Use VCG? • Good when CTRs are separable • Does not apply when CTRs are not separable • VCG: give every advertiser a discount equal to the “extra revenue” it generates Ashish Goel (ashishg@stanford.edu)

  11. Laddered auction • Rank advertisers according to rule bi£ qi. • Consider the advertiser ranked j, • For the clicks it would have received at slot j+1, charge the same per-click amount as would have been charged at the (j+1)st slot. • For any additional clicks, charge the minimum bid required to get the j-th slot. • Recursive definition Aggarwal, Goel, Motwani; EC’06 Ashish Goel (ashishg@stanford.edu)

  12. Example Top slot 30 Discount: $$$ 20 3rd slot Top slot 15 Bid/Valuation per click 4th slot 2nd slot 10 3rd slot No ad 4th slot 0 15 20 30 50 Clicks/100 impressions Ashish Goel (ashishg@stanford.edu)

  13. Properties of the Laddered auction • Theorem: For any given ranking vector, the Laddered Auction is the unique truthful auction. Ashish Goel (ashishg@stanford.edu)

  14. TruthfulnessCannot gain by moving higher or lower 30 2nd slot 20 3rd slot Top slot 15 Bid/Valuation per click 4th slot 2nd slot 10 3rd slot 4th slot 0 15 20 30 50 Clicks/100 impressions Ashish Goel (ashishg@stanford.edu)

  15. Comparison with the current auction • Nash Equilibrium: A set of bids s.t. no single bidder can gain by deviating. • Current auctions have several equilibria with different revenues. • Theorem: For separable CTRs, there exists a set of bids under the current auction s.t. • They produce the same outcome (in allocation, pricing and thus revenue) as the laddered auction. • The bids form a Nash equilibrium. Ashish Goel (ashishg@stanford.edu)

  16. Related work • When click-through rates are separable, our pricing method reduces to VCG with appropriate weights. • For the case of separable CTRs, • [Hal Varian] and [Edelman, Ostrovsky and Schwarz] show that the VCG outcome is a bidder-optimal envy-free equilibrium of the next-price auction. • [Lahaie] Truthful pricing schemes for the special case of Google and Yahoo’s ranking scheme. Ashish Goel (ashishg@stanford.edu)

  17. Summary and open problems • Current ad auctions are not truthful. • Laddered auction is the unique truthful auction in general for fixed quality vectors. • There is an equilibrium of the current auction that achieves the same outcome as the laddered auction, assuming separability. • Open problems: • Can we put the repeated nature of the auction to better use? • More general revenue equivalence • Better pricing models which take into account • budgets • information • slots Ashish Goel (ashishg@stanford.edu)

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