Internet Advertising and Optimal Auction Design

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Internet Advertising and Optimal Auction
Design Michael Schwarz Yahoo! Research Keynote
Address KDD July 2008
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Humorous History of Market Design
Wife auctions, Babylon, 5th century BC
Market design, matching theory, second half 20th
century, US
Moving from a metaphor to reality, Everywhere, now

• Note Vickrey (1961) did not invent Vickrey
  auction
• Gale, Shapley (1962) did not invent deferred
  acceptance algorithm

Over time mechanism design moved from being
primarily a metaphor describing markets to a tool
that shapes them. Indeed, mechanisms can be
viewed as models describing more or less
everything in the economy---e.g. a worker
negotiating with a few employers can be modeled
as a seller conducting an auction young man and
woman complex journey towards finding life
partners can be modeled as a deferred acceptance
algorithm etc. Literal interpretation of the
words mechanism design becomes increasingly
appropriate--- FCC conducting a spectrum auction
and medical residency match are a few examples
where mechanism design is no longer a metaphor of
reality but rather it is a force that shapes
reality of the market place with clear and rigid
rules. This in turn gave rise to a number of
interesting algorithmic and data mining problems
that are of both theoretical and practical
importance.
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Designed Mechanisms v. Metaphors in the
Internet Age

• Until recently there was a sharp distinction
  between situation were mechanism is a "metaphor
  (or a model)" vs. "designed mechanisms". In the
  former case the underlying rules of the game are
  complex and implicit---the economic reality only
  roughly resembles the simple rules of mechanism
  design models. In the later case the rules tend
  to be fairly simple and explicit.
• Recently, a new trend emerged---mechanisms that
  are designed (in a sense that the rules of the
  game are explicitly specified in a market run by
  a computer program), yet the rules of the market
  place are complex and as long as market
  participants are concerned the rules are implicit
  because they are not fully observable by market
  participants.
• The market for sponsored search is perhaps the
  first example of such marketplace-- the mechanism
  used for selling sponsored search advertisement
  is better described by words "pricing mechanism"
  than an auction. In essence, when machine
  learning meets mechanism design we end up with a
  "designed mechanism" that shares some features of
  unstructured environment of the off line world.
  As mechanism becomes enriched with tweaks based
  on complex statistical models the rules become
  complex enough to be impossible to communicate to
  market participants.

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History

• Generalized First-Price Auctions 1997 auction
  revolution by Overture (then GoTo)
• Pay per-click for a particular keyword
• Links arranged in descending order of bids
• Pay your bid
• Problem. Generalized First-Price Auction is
  unstable, because it generally does not have a
  pure strategy equilibrium, and bids can be
  adjusted dynamically

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History (continued)

• Googles (2002) generalized second-price auction
  (GSP)
• Pay the bid of the next highest bidder
• Later adopted by Yahoo!/Overture and others

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GSP and the Generalized English Auction

• N2 slots and K N 1 advertisers
• ai is the expected number of clicks in position i
• sk is the value per click to bidder k
• A clock shows the current price continuously
  increases over time
• A bid is the price at the time of dropping out
• Payments are computed according to GSP rules
• Bidders values are private information

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Strategy can be represented by pi(k,h,si)

• si is the value per click of bidder i,
• pi is the price at which he drops out
• k is the number of bidders remaining
• (including bidder i), and
• h(bk1,,bk) is the history of prices at which
  bidders K, K-1, , k1 have dropped out
• If bidder i drops out next he pays bk1
• (unless the history is empty, then set bk10).

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• Theorem. In the unique perfect Bayesian
  equilibrium of the generalized English auction
  with strategies continuous in si, an advertiser
  with value si drops out at price
• pi(k,h, si) si -(si-bk1) ak /ak-1
• In this equilibrium, each advertiser's
  resulting position and payoff are the same as in
  the dominant-strategy equilibrium of the game
  induced by VCG. This equilibrium is ex post the
  strategy of each bidder is a best response to
  other bidders' strategies regardless of their
  realized values.
• The above is from Edelman, Ostrovsky and Schwarz
  Internet Advertising and the Generalized Second
  Price Auction Selling Billions of Dollars Worth
  of Keywords, AER, March, 2007

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The Intuition of the Proof

• First, with k players remaining and the next
  highest bid equal to bk1, it is a dominated
  strategy for a player with value s to drop out
  before price p reaches the level at which he is
  indifferent between getting position k and paying
  bk1 per click and getting position k-1 and
  paying p per click.
• Next, if for some set of types it is not optimal
  to drop out at this "borderline" price level, we
  can consider the lowest such type, and then once
  the clock reaches this price level, a player of
  this type will know that he has the lowest
  per-click value of the remaining players. But
  then he will also know that the other remaining
  players will only drop out at price levels at
  which he will find it unprofitable to compete
  with them for the higher positions.

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Optimal Mechanism

• Assume that bidder values are iid draws from a
  distribution that satisfies the following
  regularity condition (1-F(v))/f(v) is a
  decreasing function of v.
• Proposition. Generalized English auction with a
  reserve price v is an optimal mechanism, where
  v denote the solution of
• (1-F(v))/f(v) v
• Note The optimal mechanism design in multi-unit
  auctions remains an open problem.
• Note Reserve price does not depend on the rate
  of decline in CTR, on the number of positions and
  on number of bidders
• From Edelman and Schwarz Optimal Auction Design
  in a Multi-unit Environment The Case of
  Sponsored Search Auctions

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Percent increase in search engine revenue when
search engines set optimal reserve prices
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Total increase in each advertiser's payment, when
reserve price is set optimally versus at 0.10

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• Theorem. Reserve price causes an equal increase
  in total payments of all advertiser whose value
  are above reserve price.

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