COS 444 Internet Auctions: Theory and Practice

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COS 444 Internet AuctionsTheory and Practice
Spring 2009 Ken Steiglitz
ken_at_cs.princeton.edu
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Mechanics

• COS 444 home page
• Classes
• - experiments
• - discussion of papers (empirical,
  theory)
• you and me
• - theory (blackboard)
• Grading
• - problem set assignments, programming
• assignments
• - class work
• - term paper

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Background

• Freshman calculus, integration by parts
• Basic probability, order statistics
• Statistics, significance tests
• Game theory, Nash equilibrium
• Java or UNIX tools or equivalent

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Why study auctions?

• Auctions are trade trade makes civilization
  possible
• Auctions are for selling things with uncertain
  value
• Auctions are a microcosm of economics
• Auctions are algorithms run on the internet
• Auctions are a social entertainment

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Cassady on the romance of auctions (1967)
Who could forget, for example, riding up the
Bosporus toward the Black Sea in a fishing vessel
to inspect a fishing laboratory visiting a
Chinese cooperative and being the guest of honor
at tea in the New Territories of the British
crown colony of Hong Kong watching the frenzied
but quasi-organized bidding of would-be buyers in
an Australian wool auction observing the
"upside-down" auctioning of fish in Tel Aviv and
Haifa watching the purchasing activities of
several hundred screaming female fishmongers at
the Lisbon auction market viewing the
fascinating "string selling" in the auctioning of
furs in Leningrad eating fish from the Seas of
Galilee while seated on the shore of that
historic body of water
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Cassady on the romance of auctions (1967)
... observing "whispered bidding in such
far-flung places as Singapore and Venice
watching a "handshake" auction in a Pakistanian
go-down in the midst of a herd of dozing camels
being present at the auctioning of an early Van
Gogh in Amsterdam observing the sale of flowers
by electronic clock in Aalsmeer, Holland
listening to the chant of the auctioneer in a
North Carolina tobacco auction watching the
landing of fish at 4 A.M. in the market on the
north beach of Manila Bay by the use of
amphibious landing boats observing the bidding
of Turkish merchants competing for fish in a
market located on the Golden Horn and answering
questions about auctioning posed by a group of
eager Japanese students at the University of
Tokyo.
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Auctions Methods of Study

• Theory (1961--)
• Empirical observation (recent on internet)
• Field experiments (recent on internet)
• Laboratory experiments (1980--)
• Simulation (not much)
• fMRI (?)

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History
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History
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History
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History
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History
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History
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History
Route 6 Long John Nebel pitching hard
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Standard theoretical setup

• One item, one seller
• n bidders
• Each knows her value vi (private value)
• Each wants to maximize her
• surplusi vi paymenti
• Values usually randomly assigned
• Values may be interdependent

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English auctions variations

• Outcry ( jump bidding allowed )
• Ascending price
• Japanese button

Truthful bidding is dominant in Japanese button
auctions
Is it dominant in outcry? Ascending price?
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Vickrey Auction sealed-bid
second-price
William Vickrey, 1961
Vickrey wins Nobel Prize, 1996
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Truthful bidding is dominant in Vickrey auctions
Japanese button and Vickrey auctions are (weakly)
strategically equivalent
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Dutch descending-price
Aalsmeer flower market, Aalsmeer, Holland, 1960s
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(No Transcript)
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Sealed-Bid First-Price

• Highest bid wins
• Winner pays her bid
• How to bid? That is, how to choose bidding
  function
• Notice bidding truthfully is now pointless!

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Dutch and First-Price auctions are (strongly)
strategically equivalent
So we have two pairs, comprising the four most
common auction forms
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Enter John Nash

• Equilibrium translates question of human behavior
  to math
• How much to shade?

Nash wins Nobel Prize, 1994
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Equilibrium

• A strategy (bidding function) is a (symmetric)
  equilibrium if it is a best response to itself.
• That is, if all others adopt the strategy,
  you can do no better than to adopt it also.

Note Cannot call this optimal
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Simple example first-price

• n2 bidders
• v1 and v2 uniformly distributed on 0,1
• Find b (v1 ) for bidder 1 that is best response
  to b (v2 ) for bidder 2 in the sense that
• E surplus max
• Note We need some probability theory for
  uniformly distributed and E

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Verifying a guess

• Assume for now that v/ 2 is an equilibrium
  strategy
• Bidder 2 bids v2 / 2 Fix v1 . What is bidder
  1s best response b (v1 ) ?
• Esurplus
• the average is over the values of v2 when 1
  wins
• Bidders 1s best choice of bid is b v1 / 2
  QED.

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and Hurwicz Myerson Maskin
win Nobel prize in 2007 for theory of mechanism
design
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New directions Simulation

• Agent-Based Simulation of Dynamic Online
  Auctions, H. Mizuta and K. Steiglitz, Winter .
• Simulation Conference, Orlando, FL, Dec. 10-13,
  2000

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New directions Sociology

• M. Shohat and J. Musch Online auctions as a
  research tool A field experiment on ethnic
  discrimination Swiss Journal of Psychology 62
  (2), 2003, 139-145

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New directions Category clustering

• Courtesy of Matt Sanders 09
• Categories connected by mutual bidders
• Darker lines mean higher probability that two
  categories will share bidders
• Categories with higher totals near center
• Color random
• Only top 25 lines by weight are shown
• Based on 278,593 recorded auctions
• from bid histories of 18,000 users