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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(No Transcript)
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Field Experiment

• Public Versus Secret Reserve Prices in eBay
  Auctions Results from a Pokémon Field
  Experiment, R. Katkar D. Lucking-Reiley, 1
  December 5, 2000.
• We find that secret reserve prices make us
  worse off as sellers, by reducing the probability
  of the auction resulting in a sale, deterring
  serious bidders from entering the auction, and
  lowering the expected transaction price of the
  auction. We also present evidence that some
  sellers choose to use secret reserve prices for
  reasons other than increasing their expected
  auction prices.

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Pros and cons of secret reserve

• Pros
• By comparison with equal open reserve, attracts
  bidding activity, which is generally good because
  1) more bidding attracts more bidders, 2)
  bidders fear winners curse less with more
  revealed information (more later, Milgrom Weber
  82),
• and so bid higher
• Cons
• Sends signal that price will be high, discourages
  entry
• Extra fee on eBay

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Field Experiment Katkar L-R 00

• 50 matched pairs of Pokémon cards
• 30 book value, open secret reserve
• Open reserve increased prob. sale 72 vs. 52
• Open reserve yielded 8.5 more revenue
• Caution these are low-priced items!
• Caution is it reasonable to match equal secret
  and open reserves? Is this the right question?
  Use low opening? Risk on high-value items ?
• Evidence of illicit transactions around eBay

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Field Experiment Katkar L-R 00

• Notice that they concluded with a notice that
  we intended to use data on bids for academic
  research, and provided contact information for
  questions or concerns.
• Do you think this affected results?

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All-Pay auction

• Heres a different kind of auction
• High bidder wins the item
• All bidders pay their bids!
• the All-Pay Auction
• Models political campaigning, lobbying, bribery,
  evolution of offensive weapons like antlers,
  etc.
• Whats your intuiton? How do you bid? Is this
  better or worse for the seller than first-price?
  Second-price?

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All-pay equilibrium

• Start with your value v
• Esurplus pr1 wins v b ( v )
• pay in
  any event
• In value space, bid as if your value z
• Esurplus vF(z)n-1 b(z)
• And set derivative to zero at zv.

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All-pay equilbrium, cont

• Differentiating and setting zv

• Integrating and using b(0)0

• Uniform-v case

Note once again, b? 0, verifying monotonicity.
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Expected rev. for uniform vs of all-pay FP
SP

• In all-pay auction, Epay bid
• Averaging over v for each bidder
• Times n bidders
• Same as SP, FP! More revenue equiv.!

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Related to all-pay War of Attrition

• Suppose two animals are willing to fight for a
  time (b1, b2). One gives up, the other wins. The
  price paid by the winner is
• min (b1, b2).
• Essentially a second-price all-pay the winner
  pays second-highest bid, losers pay their bids.

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Rev. equiv. FPSP for general distributions

• In SP auctions,
• expected revenue
• expected price paid
• expected value of second-highest bid in
  equil.

In equil. means truthful bidding in SP auctions,
of course.
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Rev. equiv. FPSP for general distributions

• In FP auctions,
• expected revenue
• n E payment of bidder 1 in equil.
• n E bfp(v1 ) pr1 wins

Now just plug in the known equil. bidding
function
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Rev. equiv. FPSP for general distributions

• and use integration by parts mercilessly,
  yielding

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• Notice that this is also the revenue for general
  distributions in the all-pay auction

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Back to eBay timing of bids

• Pro sniping (strategic)
• Avoids bidding wars
• Avoids revealing expert information
• (if you are an expert) Roth Ockenfels
  02, Wilcox 00
• Avoids being shadowed (possible?)
• Possibly conceals your interest entirely
• Ockenfels Roth 06 suggest implicit collusion
  (a weak version of the prisoners dilemma)

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Roth Ockenfels 02, Wilcox 00 Evidence from
the field

• Roth Ockenfels Computers vs. antiques
• Wilcox Power drills, etc. vs. pottery
• Bidding on collectibles later than bidding on
  commodities
• eBay bidding later than on Amazon (where deadline
  is extensible)
• Bidders with high feedback later than those with
  low feedback on eBay

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Ockenfels Roth 06 Argument pro sniping

• Suppose there is a significant chance of a snipe
  missing the deadline
• Then sniping can amount to implicit collusion,
  similar to an iterated prisoners dilemma
• ? Depends on assumption of unreliable
  sniping (?, see eSnipe, eg)

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Ockenfels Roth 06 Argument pro sniping

• Suppose two bidders, each misses deadline with
  prob. ½
• Each decides to bid truthfully
• Each decides to bid exactly once, either early or
  late (snipe)
• Each has private value 21
• Starting bid 1

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Ockenfels Roth 06 Argument pro sniping

• Game matrix, expected payoffs

Defect ?
Cooperate ?
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Ockenfels Roth 06 Argument pro sniping

• Game matrix, expected payoffs

See Axelrod, Evolution Of Cooperation,
Basic Books, NY, 1984
An iterated Prisoners Dilemma! Actually, Friend
or Foe game show because 0/0 is a weak
equilibrium
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Back to eBay timing of bids

• Pro sniping (nonstrategic)
• Delays commitment
• Or just procrastination
• Soon-to-expire may be displayed first in search
• Willingness to pay increases with time
• --- endowment effect Knetsch Sniden 84,
  Kahneman, Knetsch, Thaler 90, Thaler 94

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Back to eBay timing of bids

• Anti sniping (strategic early bidding)
• Scares away competition
• Raising ones own bid even scarier
• Rasmusen 06 suggests cost of discovery leads to
  a collusive equilibrium

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Rasmusen 06Argument pro early bidding

• Bidder 1 is uncertain of her value, can pay cost
  c to discover bidder 2 is certain of his value
• 1 starts with low bid
• 2 bids early to signal if his value is high
• 1 pays to discover her value on signal
• With carefully chosen c this is mutually
  beneficial
• --- an asymmetric equilibrium
• Do you believe this?

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Back to eBay timing of bids

• Anti sniping (nonstrategic early bidding)
• Allows you to sleep, eat, etc. (But sniping
  services and software solve this problem.)
• Psychological reward for being listed as high
  bidder
• Sniping may be perceived as underhanded,
  cowardly, unethical