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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Theory

• Order statistics
• pdf of k-th highest
• cdf of k-th highest
• Application to revenue calculation

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pdf of k-th largest
ways
n choices for which drawn
n f(x) dx
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(No Transcript)
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German tank problem
Suppose tank numbers are sequential real numbers
uniform on 0,N. We capture k tanks. The
expected max of k samples is
So a reasonable estimate is
(when values are integers, subtract 1)
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Theory

• Order statistics
• pdf of k-th highest
• cdf of k-th highest
• Simple equilibrium calculation

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Quick and dirty equilibrium calculation for FP
with iid uniform values
First price, n bidders Suppose everyone else bids
?vi
Differentiate wrt b, set to 0 ? b
(1-1/n)v1
(checks )
so ? (1-1/n) works as equilibrium
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Theory

• Order statistics
• pdf of k-th highest
• cdf of k-th highest
• Simple equilibrium calculation
• Revenue equivalence w. uniform vs

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Revenue equivalence of FP SP, uniform

• SP
• Eprice paid EY2 (n-1)/(n1)
• Evalue of winner EY1 n/(n1)
• Esurplus of winner difference 1/(n1)
• FP
• Equil. Bid is v(n-1)/n
• Esurplus of winner Evmax/n 1/(n1)

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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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Shohat Musch 03 typical field experiment
methodology

• Parallel items sold (30 DVDs), once with each
  experimental variable (mehmet.orgum vs.
  michael.ottersbach) and all other variables
  controlled as equal or randomized.
• Eg., Mehmet auctioned one randomly chosen half
  (A) the first week, and the other half (B) the
  second week Michael auctioned B the first week
  and A the second.

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Shohat Musch 03 typical field experiment
methodology

• Other variables controlled as carefully as
  possible (for example, DVDs not shipped first
  week, so no feedback appeared for either
  seller)
• Statistical tests of results (usually probability
  of observing results assuming null hypothesis gt
  95)

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Shohat Musch 03 typical field experiment
methodology

• Discussion, interpretation
• Alternative explanations (not high enough
  financial risk not social setting Mehmet not
  recognized as Turk presentation might have
  seemed German (!) buyers may turn to Turkish
  sellers only after not finding it from a German
  seller, etc.)
• Other work

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Shohat Musch 03 typical field experiment
methodology

• Privacy, ethics
• Buyers not informed, no consent!
• Data hidden after experiment (make profile
  private, anonymity guaranteed)
• Experiments kept within rules (no surveys, eg)
• Deals kept scrupulously honest

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Field experiments Testing theory

• LR 99 tests FP-Dutch and SP-English revenue
  equivalence online (pre-eBay)
• Katkar-LR 00 tests public vs. secret reserve on
  eBay
• LR 00 tests effects of reserves in FP online
  (pre-eBay)

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Lucking-Reiley 99Magic on the internet(his PhD
dissertation)

• Pre-eBay
• Tests revenue equivalence
• FPDutch and
• SPEnglish

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LR 99 (cont)

• Newsgroup rec.games.deckmaster, now an
  impossible experiment.
• 1995 6000 messages/week, highest volume on the
  internet. 90 Magic cards.
• Variety of auctions observed, all but Vickrey
• Sold matched pairs, first with FP first, then
  Dutch then with Dutch first, then FP. Similarly
  for English-SP.
• Experiments were profitable1600 purchase sold
  for 2000.

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LR 99 (cont)

• Results
• Revenue in Dutch gt FP by 30
• (opposite to lab experiments)
• Explain! (while strategically
• equilvalent)
• Revenue in English SP (while
• weakly strategically equivalent)
• Revenue equivalence between
• pairs left open

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Field results (summary of some results)

• LR 99 Revenue English SP,
• Dutch gt FP
• LR 00 open reserve in FP auctions reduces no. of
  bidders, reduces probsell , increases revenue
  conditional on selling total revenue?
• Katkar-LR 00 open reserve increases probsell
  and revenue---relative to secret reserve (eBay)