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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The common-value model

• All buyers have the same actual value, V.
• Buyers are uncertain about this value thus not
  private values. Efficiency not relevant.
• Buyers estimate values variously, by consulting
  experts, say. We say they receive noisy signals
  that are correlated with the true value.
• In a popular special case, buyers receive the
  signals si V ni , where ni is a zero-mean
  random process common to all buyers.
• We can think of real-world bidders as living in
  the range between IPV and common-value.

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Winners Curse

• The paradigmatic experiment bid on a jar of
  nickels
• The systematic error is to fail to take into
  account the fact that
• winning may be an informative event!
• A persistent violation of the beloved hypothesis
  of homo economicus, the rational self-interested
  actor. Can be considered a cognitive illusion

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From the archives
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Buy-a-Company experiment

• R.H. Thaler, The Winners Curse, 1992 reports
  the unpublished results of Weiner, Bazerman,
  Carroll, 1987 with Bidding for Paramount.
• 69 NWU MBA students played the game 20 rounds
  each, with financial incentives and feedback
  after each trial.
• ? 5 learned to bid 1 by end,
• after avg. of 8 trials
• ? No sign of learning among the others!

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Winners Curse, references

• Seminal paper E.C. Capen, R.V. Clapp, W.M.
  Campbell, Competitive bidding in high-risk
  situations, J. Petroleum Technology, 23, 1971,
  pp. 641-653.

See R. Thaler, The Winners Curse Paradoxes and
Anomalies of Economic Life, Princeton Univ.
Press, 1992. J.H. Kagel and D. Levin, Common
value auctions and the Winners curse, Princeton
Univ. Press, 2002.
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Claims of Winners Curse in the field

• Oil industry
• Book publication rights
• Professional baseball free-agent market
• Blecherman
  Camerer 96
• Corporate takeover battles
• Real-estate auctions
• Stock market investments, IPOs
• Blind bidding by movie exhibitors
• Construction industry etc.
• but difficult to prove using field data
  because of the existence other factors

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• What do you do if you find your competitors are
  making consistent errors?

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• What do you do if you find your competitors are
  making consistent errors? Publish. Share your
  knowledge. --- this lowers bids!
• Thaler, pp. 61-62, after Julia Grant

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• What do you do if you find your competitors are
  making consistent errors? Publish. Share your
  knowledge. --- this lowers bids!
• Thaler, pp. 61-62, after Julia Grant
• When to share information and when to hide it?

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First laboratory experiment

• M.H. Bazerman and W.F. Samuelson, I won the
  auction but I dont want the prize, J. Conflict
  Resolution, 27, pp. 618-34, 1983.
• M.B.A. students, Boston University
• Four first-price sealed-bid auctions
• 800 pennies 160 nickels 200 large paper clips _at_
  4 400 small paper clips _at_ 2.
• All thus worth V 8.00.

Kagel Levin 02
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?Shade?
Curse
From Bazerman Samuelson 83
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Bazerman and Samuelson 83

• Bidders were asked for estimates as well as bids.
  48 auctions were run altogether.
• Average estimate was 5.13 8 2.87
• Average winning bid was 10.01 8 2.01
• The experimental design was sophisticated,
  subjects were told they were competing against
  different numbers of bidders, and the effects of
  uncertainty and group size measured

Kagel Levin 02
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Winning may be bad news, unless you shade
appropriately

• Suppose bidders are uncertain about their values
  vi , receiving noisy signals si
• Based on this information, your best estimate of
  your true value, after receiving the signal six,
  is
• EV s1x
• Suppose you, bidder 1, win the auction!
• Then your new best estimate of your value is EV
  s1x , Y1 lt x lt EV s1x --- where Y1 is
  the highest of the other signals

Intuitive argument Krishna 02. Conditions
for proof?
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In first-price auctions

• Suppose n number of bidders increases.
• According to the private-value equilibrium, you
  should increase your bid
• Taking into account the Winners Curse, you
  should decrease your bid (effect can dominate).
  Having the highest estimate among 5 bidders is
  not as bad as among 50.
• ? Note that in any common-value auction,
  the winners curse results from a miscalculation,
  and does not occur in equilibrium so what is
  that equilibrium?

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Winners curse, cont

• Important paper, which describes how to find a
  symmetric equilibrium in one general setting
• R.B. Wilson, Competitive Bidding with
  Disparate Information, Management Science 15, 7,
  March 1969, pp. 446-448.
• That is, how to compensate for the tendency to
  forget how likely it is for winning to be bad
  news, in equilibrium.

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Example FP common-value, uncorrelated signals

• Take the simple 2-bidder example where the true
  value of a tract is V v1 v2 , where v1 , v2
  amount of oil on parts 1, 2 of a tract. Bidder i
  knows vi with certainty, but not the other. The
  vis are uniform iid on 0,1.
• What is the equilbrium bid? Is it a good bid?
• How does this FP auction compare to the
  corresponding SP for the sellers revenue?

From F.M. Menezes P.K. Monteiro, An Intro. to
Auction Theory, Oxford Univ. Press, 2005.
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Winning may be bad news example

• In this common-value model V v1 v2
• EV v1 v1 ½
• EV v1 (v2 v1) v1 Ev2 v2 v1
• v1 v1 /2
• v1 ½
• EV v1

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Example FP common-value, uncorrelated signals
Menezes Monteiro 05

• Well look for a symmetric, differentiable, and
  increasing equil. bidding fctn. b(v) . As usual,
  suppose bidder 1 bids as if her value is z. Her
  expected surplus (profit) is
• The equilibrium condition is

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Example FP common-value, uncorrelated signals
Menezes Monteiro 05

• This differential equation is of a familiar,
  linear type
• Integrate from 0 to v, letting b(0) b0 . Note
  we cant assume b0 0 Why not?
• Argue from finiteness of b(0) that c 0.
• So

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Example FP common-value, uncorrelated signals
Menezes Monteiro 05

• Notice that bidder i never pays more than the
  true value V . .
• But now suppose signals vi are distributed as F
  on 0,1, instead of being uniform. Exactly the
  same procedure gets us the symmetric equilibrium
• is this always increasing?
• Take the special case F v? , where ? gt 0.

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Example FP common-value, uncorrelated signals
Menezes Monteiro 05

• The symmetric equilibrium then becomes
• If ? gt 1, the winning bidder may well bid higher,
  and hence pay more than, the true value V . Is
  this an example of the Winners Curse?

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Example SP common-value, uncorrelated signals
Menezes Monteiro 05

• In the SP auction with this common-value model,
  the equilibrium in the uniform case, using the
  same technique, is b(v) 2v.
• This may be higher than the true value V, and the
  winner may very well pay more than V. In fact,
  she may pay more than the expected value of V
  conditional on having the highest bid. What is
  that? Again, is this an example of the Winners
  Curse?

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Example common-value, uncorrelated signals
Menezes Monteiro 05

• It turns out that the FP and SP auctions with
  this common-value model are revenue equivalent.
  In fact, this is generally true for common-value
  cases with independent signals Menezes
  Monteiro 05, pp. 117ff .
• But revenue equivalence finally breaks down when
  the signals are correlated.

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Kagel Levins Experimental work
J.H. Kagel and D.Levin, Common value auctions
and the Winners curse, Princeton Univ. Press,
2002

• Kagel Levin et al. did a lot of laboratory
  experimental work with this model
• Choose the common value x0 from the uniform
  distribution uniform on xL, xH,
• known to the bidders. The bidders are given
  signals drawn uniformly and independently from
  xoe, xoe, where e is known to the bidders.
• The signals in this case are correlated.

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Dyer et al.s comparison between experienced
inexperienced bidders
D. Dyer, J.H. Kagel, D. Levin, A Comparison
of Naïve Experienced Bidders in Common-Value
Offer Auctions A Laboratory Analysis, Econ. J.,
99, 108-115, March 1989.

• Experiment was a procurement auction one buyer,
  many sellers, so low bid wins
• Common-value model analogous to the ones in the
  Kagel-Levin experiments
• Compares performance of Univ. Houston Econ majors
  with executives in local construction companies
  with average of 20 years experience of bid
  preparation

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D. Dyer, J.H. Kagel, D. Levin, A Comparison
of Naïve Experienced Bidders in Common-Value
Offer Auctions A Laboratory Analysis, Econ. J.,
99, 108-115, March 1989.

• Results
• Winners curse extends to procurement (offer)
  auctions
• Winners curse extends to auctions with only 4
  bidders
• No significant difference in performance between
  undergrads and professionals!
• 
  Explain?

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• ?Executives didnt take the experiment seriously?
• Executives auctions in practice have a strong
  private-value component (overhead, opportunity
  costs), and losses can be mitigated by
  renegotiation, or change-orders?
• Dyer et al. conclude, however, that executives
  have learned a set of situation specific rules of
  thumb which permit them to avoid the winners
  curse in the field but which could not be applied
  in the lab.
• (by feedback or selection)
• Learning occurs Not through understanding and
  absorbing the theory, but from rules of thumb
  that are likely to breakdown under extreme
  changes, or truly novel, economic conditions.

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Next

• Common-value auctions lead to the next, and most
  general treatment of single-item auctions,
  Milgrom Weber 82.
• The model here is called the affiliated values
  model, and represents a spectrum, with IPV at one
  extreme, and common-value at the other. Most
  auctions have elements of both.
• To wrap up the Winners Curse

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• Capen et al.s fortune cookie
• He who bids on a parcel what he thinks it is
  worth, will, in the long run, be taken for a
  cleaning.

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Milgrom Weber 1982
affiliated values Revenue ranking,
but only with symmetric bidders
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Interdependent Values

• In general, we relax two IPV assumptions
• Bidders are no longer sure of their values (as in
  the common-value case discussed in connection
  with the Winners Curse)
• Bidders signals are statistically correlated
  technically positively affiliated (see Milgrom
  Weber 82, Krishna 02)
• Intuitively if some subset of signals is
  large, its more likely that the remaining
  signals are large

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Major results in Milgrom Weber 82

• For the general symmetric, affiliated values
  model
• English gt 2nd -Price gt 1st -Price Dutch
  (revenue ranking)
• If the seller has private information, full
  disclosure maximizes price (Honesty is the best
  policy in the long run)

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Milgrom Weber 82 Caveats

• Symmetry assumption is crucial results fail
  without it
• English is Japanese button model
• For disclosure result seller must be credible,
  pre-committed to known policy
• Game-theoretic setting assumes distributions of
  signals are common knowledge

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The linkage principle (after Krishna 02)

• Consider the price paid by the winner when her
  signal is x but she bids as if her value is z ,
  and denote this price by W (z , x).
• Define the linkage
• sensitivity of expected price paid by winner
  to variations in her received signal when bid is
  held fixed

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The linkage principle, cont
Result Two auctions with symmetric and
increasing equilibria, and with W(0,0) 0, are
revenue-ranked by their linkages. Consequences
1st -Price linkage L1 0 2nd -Price price
paid is linked through x2 to x1
so L2 gt 0 English through all signals to x1
so LE gt L2 gt L1
?
revenue ranking