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					COS 444
Internet Auctions:
Theory and Practice

         Spring 2008

         Ken Steiglitz

week 5                          1
Some details of eBay’s Algorithm
    Normal case (assume tick = $1) :
     $20 ......... high bid

         12 ……… minimum allowable bid
         11 ……… posted (will be paid)
         10 ……… second-highest bid

week 5                                  2
Some details of eBay’s Algorithm
    Suppose next bid is $19.90 :
     $21 ......... minimum allowable bid
      20 ……… high bid (posted, paid)
      19.90 .... second-highest bid

week 5                                     3
Some details of eBay’s Algorithm
    Suppose next bid is, instead, $20.10 :
     $21.10 …. minimum allowable bid
      20.10 …. high bid (posted, paid)
      20 ……… second-highest bid

If now high bidder raises her bid to
   $21.10 or higher, her posted price ---
   which she would pay, goes up!
   This is basis of a law suit
week 5                                        4
A slick way to derive equilibrium: use
  value space
We assume a 1-1 bidding function b(v) .

Then if bidder 1 bids b(z), the
 equilibrium condition is that surplus be
 maximized when z = v1 .

This corresponds to bidding b(v1 ) .
week 5                                      5
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                                                    6
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.
   Open reserve yielded 8.5% more revenue
   Caution: these are low-priced items!
   What are possible pros of secret reserve?
   Evidence of illicit transactions around eBay
week 5                                             7
 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,…

What’s your intuiton? How do you bid? Is this
 better or worse for the seller than first-price?
 week 5                                             8
 Theory: all-pay auction
 Start with

E[surplus] = pr[1 wins][ v1 ] – b ( v1 )

… equilibrium

week 5                                     9
 Praxis: Reasons to snipe
 Avoids bidding wars
 Avoids revealing expert information
   (if you are an expert)
 Avoids being shadowed
 Possibly conceals your interest entirely
 Ockenfels & Roth (2006) suggest
  implicit collusion (prisoner’s dilemma)

 Avoids early commitment
week 5                                       10
Praxis: Reasons to bid early
   Scaring away competition
   Raising one’s own bid even scarier
   Impatience, anxiety, pride
   Rasmusen (2006) suggest cost of discovery
    leads to a collusive equilibrium
   Allows you to sleep, eat, etc. (But sniping
    services and software solve this problem.)

week 5                                            11
Praxis: Field studies of early
and late bidding
   Roth & Ockenfels papers
   eBay, Amazon, and Yahoo rules
    (Yahoo now out of the auction business)

    Open Problem: How can a seller encourage
     early bidding?

week 5                                         12

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