Transcript Internet Advertising and Optimal Auction Design Michael Schwarz Yahoo! Research NIPS Workshop: Beyond Search: Computational Intelligence for the Web December 2008

Internet Advertising and
Optimal Auction Design
Michael Schwarz
Yahoo! Research
NIPS Workshop: Beyond Search:
Computational Intelligence for the Web
December 2008
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Four for One Special
• Optimal Auction Design in a Multi-unit Environment: The
Case of Sponsored Search Auctions (with Edelman)
Main topic of this talk
• Internet Advertising and the Generalized Second Price
Auction: Selling Billions of Dollars Worth of Keywords,
(with Edelman, Ostrovsky) AER, March, 2007
• Greedy Bidding Strategies for Keyword Auctions (with Cary
et al.), EC 2007
• Ad Auction Design and User Experience, (with Abrams),
Special Issue of Applied Economics Research Bulletin on
Theoretical, Empirical, and Experimental Research on
Auctions, 2007
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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
(second price) auction
•Gale, Shapley (1962) did not invent deferred
acceptance algorithm
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Over time mechanism design moved from being primarily a
metaphor describing markets to a tool that shapes them
Everything in the economy is a mechanism e.g.:
• A worker negotiating with employers can be modeled as an
auction
• Matting can be modeled as a deferred acceptance algorithm
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Mechanism Design–
Literal Interpretation
• Literal interpretation of words
“mechanism design” are increasingly
appropriate
• FCC conducting a spectrum auctions
• Medical residency match is a reality
• 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
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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.
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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.
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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)
• Google’s (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
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N≥2 slots and K = N +1 advertisers
αi 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=(bk+1,…,bk) is the history of prices at which
bidders K, K-1, …, k+1 have dropped out
If bidder i drops out next he pays bk+1
(unless the history is empty, then set bk+1≡0).
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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-bk+1) αk /αk-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
Cary et al. EC 2007, shows that myopic best bidding strategies converge to
the same equilibrium.
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The Intuition of the Proof
First, with k players remaining and the next highest bid equal to bk+1, 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 bk+1
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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Yahoo! Research is not Just About
Sponsored Search
• Median Stable Matching (with Yenmez)
• Standard two sided matching market with
wages (in discrete increments)
• There exists finite set of stable matches
(buyer and seller optimal matches are
extreme points of this set)
• We show that median stable match exists
i.e. a match that is median for every agent at
the same time
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