laddered auction

Laddered auction

Ashish Goeltanford

Universityhttp://www.stanford.edu/~ashishg

Based on slides by Gagan Aggarwal

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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.

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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).

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10

20 30 50

Bid

/clic

k

Example

14

20

30

0 15

3rd slot

2nd slot

3rd s

lot

2n

d sl

ot

To

p s

lot

4th s

lot

Clicks/100 impressions

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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.

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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 asProfit = valuation - price

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10

20 30 50

Bid

/Va

lua

tion

pe

r cl

ick

Example

14

20

30

0 15

3rd slot

2nd slot

Clicks/100 impressions

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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 andan advertiser-specific factor.

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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

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10

20 30 50

Example

15

20

30

0 15

No ad

4th slot

3rd slot

Top slot

Bid

/Va

lua

tion

pe

r cl

ick

3rd s

lot

2n

d sl

ot

To

p s

lot

4th s

lot

Clicks/100 impressions

Discount: $$$

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Properties of the Laddered auction

Theorem:

For any given ranking vector, the Laddered Auction is the unique truthful auction.

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10

20 30 50

TruthfulnessCannot gain by moving higher or lower

15

20

30

0 15

4th slot

3rd slot

2nd slot

3rd s

lot

2n

d sl

ot

To

p s

lot

4th s

lot

Bid

/Va

lua

tion

pe

r cl

ick

Clicks/100 impressions

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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.

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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.

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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