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

Ashish Goel (ashishg@stanford.edu) 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) 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. 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Next-price auction A.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). 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) Example 30 2nd slot 20 3rd slot Top slot Bid/click 14 2nd slot 10 We will consider ranking by bid. Also applies to ordering by weighted bid if we fold in the weight into the bid. Fix others’ bids and shown them on the y-axis. That defines bid thresholds at which Alice’s slot changes. X-axis shows the number of clicks she receives at a given slot. Consider an example with weights equal to 1. All examples with weight 1. 3rd slot 4th slot 15 20 30 50 Clicks/100 impressions 9/22/2018 Ashish Goel (ashishg@stanford.edu)

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. 9/22/2018 Ashish Goel (ashishg@stanford.edu)

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 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) Example 30 2nd slot 20 3rd slot 14 Bid/Valuation per click 10 15 20 30 50 Clicks/100 impressions 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) 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 CTR separates into a position-specific factor and an advertiser-specific factor. Even the savvy advertisers unable to bid optimally due to budget smoothing. We can use VCG – paerticularly good when CTRs are separable. 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) 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 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) Example Top slot 30 Discount: $$$ 20 3rd slot 15 Top slot Bid/Valuation per click 4th slot 2nd slot 10 3rd slot No ad 4th slot 15 20 30 50 Clicks/100 impressions 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Properties of the Laddered auction Theorem: For any given ranking vector, the Laddered Auction is the unique truthful auction. 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Truthfulness Cannot 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 15 20 30 50 Clicks/100 impressions 9/22/2018 Ashish Goel (ashishg@stanford.edu)

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. 9/22/2018 Ashish Goel (ashishg@stanford.edu)

Ashish Goel (ashishg@stanford.edu) 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. 9/22/2018 Ashish Goel (ashishg@stanford.edu)

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 9/22/2018 Ashish Goel (ashishg@stanford.edu)