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					               COS 444
          Internet Auctions:
         Theory and Practice

           Spring 2009

           Ken Steiglitz
           ken@cs.princeton.edu

week 5                            1
week 5   2
                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.”
week 5                                                    3
         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 “winner’s 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

week 5                                           4
         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

week 5                                             5
         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?


week 5                                        6
                  All-Pay auction
    • Here’s 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.

    • What’s your intuiton? How do you bid? Is this
      better or worse for the seller than first-price?
      Second-price?
week 5                                                   7
           All-pay equilibrium

    Start with your value = v
       E[surplus] = pr{1 wins} [ v ] – b ( v )
                               pay in any event

    In value space, “bid as if your value = z”
         E[surplus] = vF(z)n-1 – b(z)
    And set derivative to zero at z=v.

week 5                                           8
               All-pay equilbrium, con’t
• Differentiating and setting z=v:
            (n  1) v F (v)       n2
                                        f (v)  b(v)  0
• Integrating and using b(0)=0:
                                  v
                     b(v)   y dF ( y)       n 1
                                  0

 • Uniform-v case:
                 v                             v                    1
         b(v)   yd ( y   n 1
                                  )  ( n  1)  y   n 1
                                                            dy  v 1  
                                                                 n
                0                             0
                                                                    n
          Note: once again, b΄ > 0, verifying monotonicity.
week 5                                                                      9
         Expected rev. for uniform v’s
             of all-pay = FP = SP
• In all-pay auction, E[pay] = bid
• Averaging over v for each bidder:
                 1n   1 n    1  n 1
             
             0        n
                        v dv        
                              n  n 1
• Times n bidders:
                                n 1
                  E[revenue]
                                n 1

• Same as SP, FP! More revenue equiv.!

week 5                                    10
         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.

week 5                                          11
Rev. equiv. FP=SP for general distributions
• In SP auctions,
   expected revenue
     = expected price paid
     = expected value of second-highest bid in equil.
                            1                1
           Rsp  E[Y2 ]   xdG2 ( x)  1  G2 ( x)dx
                           0                0


      In equil. means truthful bidding in SP
      auctions, of course.


 week 5                                                   12
Rev. equiv. FP=SP for general distributions
• In FP auctions,
   expected revenue
     = n E [payment of bidder 1 in equil.]
     = n E [bfp(v1 ) pr{1 wins} ]
                     1
           R fp  n b fp (v) F (v) dF (v)
                                        n1
                     0

 Now just plug in the known equil. bidding function:
                                 v
                                 ydF ( y)
                                                    n1

                   b fp   (v)  0
                                              n1
                                     F (v )
 week 5                                                   13
Rev. equiv. FP=SP for general distributions

… and use integration by parts mercilessly, yielding

                1 v
    R fp  n    ydF ( y)
                                 n1
                                       dF (v)
             0 0

                      1                         1
          1  n F       n1
                                dv  (n 1) F dv   n
                      0                         0

                 1
          1   G2 dv  Rsp
                 0


week 5                                                  14
Notice that this is also the revenue for general
 distributions in the all-pay auction

                     1 v
         R fp  n        ydF ( y)
                                      n1
                                            dF (v)
                 0 0


                     1
              n bap (v)dF (v)
                     0




week 5                                               15
         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 prisoner’s
    dilemma)
week 5                                             16
         [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
week 5                                           17
          [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 prisoner’s
  dilemma

 Depends on assumption of unreliable
 sniping (?, see eSnipe, eg)

week 5                                        18
          [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

week 5                                       19
               [Ockenfels & Roth 06]
               Argument pro sniping
          Game matrix, expected payoffs

                           early late
            Defect  early  0 / 0 10 / 0
         Cooperate  late  0 / 10 5 / 5


week 5                                     20
             [Ockenfels & Roth 06]
             Argument pro sniping
         Game matrix, expected payoffs

                   early late
             early 0 / 0 10 / 0
                                   See Axelrod, Evolution
              late 0 / 10 5 / 5    Of Cooperation, Basic
                                   Books, NY, 1984

         An iterated Prisoner’s Dilemma!
         Actually, “Friend or Foe” game show
week 5
         because 0/0 is a weak equilibrium           21
         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]



week 5                                           22
         Back to eBay: timing of bids

   Anti sniping (strategic early bidding):
   • Scares away competition
   • Raising one’s own bid even scarier
   • [Rasmusen 06] suggests cost of
     discovery leads to a collusive
     equilibrium



week 5                                       23
              [Rasmusen 06]
         Argument 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?

week 5                                               24
           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




week 5                                               25

				
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