COS 444 Internet Auctions: Theory and Practice

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COS 444 Internet AuctionsTheory and Practice
Spring 2008 Ken Steiglitz
ken_at_cs.princeton.edu
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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!
• Caused by a cognitive illusion
• See Richard Thalers The Winners Curse
  Paradoxes and Anomalies of Economic Life,
  Princeton University Press, 1992.

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Winning is bad news, unless you shade

• Suppose bidders are uncertain about their values
  Vi , receiving noisy signals Xi
• Based on this information, your best estimate is
  EV X1
• Suppose you, bidder 1, win the auction!
• Then your new best estimate of your value is EV
  X1 , Y1 lt X1 lt EV X1 --- where Y1 is the
  highest of the other signals

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Example first-price auctions

• Common-value model say the item has the same but
  unknown value to all bidders, and each bidder
  receives a noisy signal related to the true value
• Suppose the number of bidders increases. Then
• According to the private-value
  equilibrium, you should increase your bid
• Taking into account the Winners Curse, you
  should decrease your bid (often dominates)

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Winners curse, cont

• Important paper, which describes how to find a
  symmetric equilibrium
• 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

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Empirical results

• In the laboratory the Winners Curse is real and
  persistent
• Observed in practice oil industry, baseball free
  agents, book publishing
• Even professional bidders from the commercial
  construction industry succumb (Dyer at al.
  suggest they learn situation-specific rules
  rather than the right theory Thaler, p. 56 )
• What do you do if you find your competitors are
  making consistent errors? Publish! Thaler, pp.
  61-62, after Julia Grant

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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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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)
• 2) 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

• 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)

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Milgrom Weber 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 ,
  denoted 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
Proposition 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 L2gt L1