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 \noindent
    { {\bf Strategic Implications of Uncertainty Over One's Own
Private Value in Auctions }   }

 

 \noindent
Eric Rasmusen,     erasmuse@indiana.edu. June 23, 2002
\\
Php.indiana.edu/$\sim$erasmuse. 
Php.indiana.edu/$\sim$erasmuse/papers/auction.pdf.  
 
\noindent
  {\bf Things to Explain}

 \noindent
1.
  Why  bidders    would like
to
know how much other  bidders are going to bid.

 \noindent
2.
 How other bidders  can benefit when an uninformed bidder learns his
value
more precisely.

 \noindent
3.
 How improved buyer information on the value of the object   hurts
the seller.


 \noindent
4.
   Why bidders update the   bid ceilings they submit  during 
the course of an auction such as those on Ebay and Amazon  that uses
proxy bidding.

 \noindent
5.
   Why bidders use ``pre-emptive bids'', bidding early  in auctions
rather than later.


 \noindent
6.
  Why bidders use ``sniping''---  the practice of  submitting bids at
the last minute.

\bigskip
 
 
\noindent
 {\bf The Model.} The  two players  in an auction  are both risk-
neutral and have
private  values which  are statistically independent and distributed
over the same support $[0,z]$, on which the densities are strictly
positive.  Bidder 1 has value $u$ distributed
according to  the atomless density $f(u)$.
Bidder 2 has value $v$
distributed according to  the atomless density $g(v)$.
 Bidder 1  knows neither  $u$
nor $v$.   At any time  he may, unobserved by Bidder 2,  pay $c$ and
learn  $u$ after additional time $\delta$ has passed. Bidder 2 knows
$v$,  but not $u$.

We will look at three sets of auction rules: a sealed-bid second-price
auction,
an Amazon auction, and an Ebay auction. In each, a player submits his
``bid ceiling'', but the winner pays the second-highest bid ceiling
submitted.
The Amazon auction has a ``soft deadline,'' ten minutes after the last
bid ceiling update.
 The Ebay auction has a ``hard deadline'': at a preannounced time. 

 If Bidder 1 is ``naive'' he is not aware that Bidder 2 is present at
the auction,i.e. he assigns probability zero to that event.

\bigskip
  
\noindent
{\bf Example 3.}
  Let   Bidder 1 have a private value $u$ uniformly distributed on [0,
100]. He can take  5 minutes and  pay  amount 5 to discover his value
precisely if he wishes; otherwise, his estimate is 50.  Bidder 1 is
naive. Let   Bidder 2
have a value  $v$ of either 10 or 60, with equal probability.

Bidder 1 will  submit  a bid ceiling of   50. Bidder 2 will submit a
bid ceiling of  10 if $v=10$, and timing will not matter. If $v=60$,
though, he should wait  until within 5   minutes of the deadline and
submit   a bid ceiling  of 60. He will win at  a price of 50, for a
payoff of  10.

What if Bidder 2  were to submit a bid ceiling of    60 earlier?
Bidder 1's payoff from paying 5 to discover $u$ would be $-5+ .6 (0) +
.4[(Eu|u>60)-60] = -5 + .4(80-60)= -5+ 8 =3,$ compared to  a payoff of
0 from not discovering his value and retaining his bid ceiling of 50.
Thus, Bidder 1 would pay to discover his value and with probability .4
he would increase his bid ceiling to  more  than 60 and win the
auction. $\pi_2=.6(60-50) + .4(0) = 6$, less than the 10  Bidder 2
would get  from   delaying his bid submission and sniping.


   
 
 
 

 

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