COS 444
Internet Auctions:
Theory and Practice
Spring 2009
Ken Steiglitz
ken@cs.princeton.edu
week 10
1
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.
week 10
2
Winner’s 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”
week 10
3
From the
archives
week 10
4
Buy-a-Company experiment
• [R.H. Thaler, The Winner’s 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the unpublished results of Weiner, Bazerman, &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!
week 10
5
Winner’s 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 Winner’s Curse: Paradoxes
and Anomalies of Economic Life, Princeton Univ.
Press, 1992.
J.H. Kagel and D. Levin, Common value auctions
and the Winner’s curse, Princeton Univ. Press,
2002.
week 10
6
Claims of Winner’s 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
week 10
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• What do you do if you find your
competitors are making consistent
errors?
week 10
8
• 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]
week 10
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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?
week 10
10
First laboratory experiment
M.H. Bazerman and W.F. Samuelson, “I won the
auction but I don’t 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
@ 4¢; 400 small paper clips @ 2¢.
All thus worth V = $8.00.
week 10
[Kagel & Levin 02]
11
Shade
Curse
From Bazerman & Samuelson 83
week 10
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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
week 10
[Kagel & Levin 02]
13
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 si=x, is
E[V | s1=x ]
• Suppose you, bidder 1, win the auction!
• Then your new best estimate of your value is
E[V | s1=x , Y1 < x ] < E[V | s1=x ] --- where Y1 is
the highest of the other signals
week 10
Intuitive argument: [Krishna 02].
Conditions for proof?
14
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 Winner’s 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 winner’s curse results from a
miscalculation, and does not occur in
equilibrium… so what is that equilibrium?
week 10
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Winner’s curse, con’t
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.
week 10
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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 vi’s 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 seller’s revenue?
*From F.M. Menezes & P.K. Monteiro, An Intro. to
Auction Theory, Oxford Univ. Press, 2005.
week 10
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Winning may be bad news: example
• In this common-value model: V = v1 + v2
• E[V | v1 ] = v1 + ½
• E[V | v1 & (v2 ≤ v1) ] = v1 + E[v2 | v2 ≤ v1 ]
= v1 + v1 /2
≤ v1 + ½
= E[V | v1 ]
week 10
18
Example: FP common-value, uncorrelated signals
[Menezes & Monteiro 05]
• We’ll 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
z
 1   [v  y  b( z )]dy
0
 vz  z 2 / 2  zb ( z )
• The equilibrium condition is
 1
 v  v  b(v)  vb(v)  0
z z v
week 10
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Example: FP common-value, uncorrelated signals
[Menezes & Monteiro 05]
• This differential equation is of a familiar,
linear type:
d [vb]
 2v
vb(v)  b  2v 
dv
• Integrate from 0 to v, letting b(0) = b0 . Note:
we can’t assume b0 = 0 … Why not?
vb(v)  v 2  c
• Argue from finiteness of b(0) that c= 0.
… So
b (v )  v
week 10
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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
v
2  y dF ( y )
b (v )  0
F (v )
[…is this always increasing?]
• Take the special case F = vθ , where θ > 0.
week 10
21
Example: FP common-value, uncorrelated signals
[Menezes & Monteiro 05]
• The symmetric equilibrium then becomes
b (v ) 
2
v
 1
• If θ > 1, the winning bidder may well bid
higher, and hence pay more than, the true
value V . …Is this an example of the
Winner’s Curse?
week 10
22
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 Winner’s Curse?
week 10
23
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.
week 10
24
Kagel & Levin’s Experimental work
[J.H. Kagel and D.Levin, Common value auctions and
the Winner’s 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 [xo–ε, xo+ε], where ε is known to the
bidders.
• The signals in this case are correlated.
week 10
25
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
week 10
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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:
• Winner’s curse extends to procurement
(offer) auctions
• Winner’s curse extends to auctions with only
4 bidders
• No significant difference in performance
between undergrads and professionals!
…Explain?
week 10
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Executives didn’t 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 winner’s 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.”
week 10
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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 Winner’s Curse:
week 10
29
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.”
week 10
30
Milgrom & Weber 1982
affiliated values
Revenue ranking, but only with symmetric bidders
week 10
31
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 Winner’s Curse)
Bidders’ signals are statistically correlated;
technically positively affiliated (see Milgrom
& Weber 82, Krishna 02)
Intuitively: if some subset of signals is large,
it’s more likely that the remaining signals are
large
week 10
32
Major results in Milgrom & Weber 82
For the general symmetric, affiliated
values model:
• English > 2nd -Price > 1st -Price =
Dutch (“revenue ranking”)
• If the seller has private information, full
disclosure maximizes price (“Honesty
is the best policy” … in the long run)
week 10
33
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
week 10
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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 :
W ( z, x)
L( x ) 
x
zx
= sensitivity of expected price paid by winner
to variations in her received signal when bid
is held fixed
week 10
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The linkage principle, con’t
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 > 0
English: … through all signals to x1 ; so
LE > L2 > L1
week 10
 revenue ranking
36