Laddered auction

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Laddered auction

• Ashish Goel

tanford University
http//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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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
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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 as
• Profit valuation - price

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Example
30
2nd slot
20
3rd slot
14
Bid/Valuation per click
10
0
15
20
30
50
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

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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
  j1, charge the same per-click amount as would
  have been charged at the (j1)st slot.
• For any additional clicks, charge the minimum bid
  required to get the j-th slot.
• Recursive definition

Aggarwal, Goel, Motwani EC06
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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
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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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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
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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 Yahoos 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