First, the rational bidder's reservation price for a
particular
item in a category he collects might depend on whether or not he
will turn out to be winning bidder on other similar items during the
budget period. If so, he would determine his reservation price,
and put in his bid, as late as possible, after he has checked out
all the upcoming auctions in his category.
Second, there is the strategy of trying to be highest bidder
at a price lower than the seller's reserve price, in a situation where
the bidder's true maximum price is higher than the seller's reserve.
With a highest bid that falls in this niche, the high bidder can
bargain with the seller by e-mail in an effort at getting the item at
a price higher than the high bid but a little lower than the seller's
reserve. This strategy depends on being able to guess the seller's
reserve and also upon the seller's being irrational in the sense of
being willing to sell at a price slightly below his own reserve.
With this strategy, if this bidder's initial bid turns out not to be
the highest bid, he will bid again. Alternatively, he might wait
and put in his bid in the last minutes.
Barbara Brown
PaceUniversity/Pleasantville
>Roger McCain wrote:
>
>> It seems to me that the EBAY proxy-bid auction lends itself to a nice
game
>> theory example -- with the complication that EBAY users don't seem to
bid
>> rationally. I'll follow up on that when I have a little more time
....
>
>I am curious to hear Roger McCain's follow-up.
>
Right. Here goes.
(I just got my week-end work product off by e-mail, so I guess if I am
going to have time, it's now).
What I have followed are collectible auctions -- items that may not be
unique, but are rare and have only subjective value. Thus, I think of
them
as private value auctions.
The rules are that the highest bidder gets the item, if it clears any
reserve price, one tick over the second-highest bid. The amount of the
tick
-- that is, the minimum bid rise -- increases with the amount bid. The
bidder gives an upper limit, and the software raises the previous if any
by
one tick. Example: the current bid is 6.50 and a tick is 50c. I put in a
maximum of 17.55 and the bid registered for me is 7.00. Exception: if
the
reserve has not been met, and my maximum is greater, then the bid
entered
is the reserve. In the previous example, if the reserve is 8.50, then
the
bid entered for me is 8.50. If, subsequently, someone overbids my
registered bid, but comes in under my maximum, the software registers a
bid
for me one tick over the competitive bid. Continuing the example, if
Robert
comes in with a bid of 14.00, the software will enter my bid of 14.50,
and
if then there is no further bidding, I buy the tiem for 14.50 -- one
tick
over the highest competing bid.
Note in passing 1) that this approximates a second-price auction, and 2)
that the economic principles have been written into the software. This
is
the future, friends.
Conjecture: the unique Nash-equilibrium occurs when everyone bids their
reservation price as soon as possible.
A) I can lose nothing by bidding my reservation price, since I don't
want
the item at a higher price and cannot in any case get it for less than
one
tick over the second-highest reservation price <ital> provided that
everyone else bids their reservation price. </ital> Thus bidding the
reservation price is the best response to the best-response strategies
of
others.
B) If I delay, I risk the possibility that someone else will enter a
maximum less than my maximum by an amount less than one tick. In the
previous numerical example, suppose Robert had bid 17.35 before I bid. I
cannot then overbid him with less than 17.85, but that is more than my
reservation price, so I do not buy the item; but, had I gotten in first,
I
would have gotten the item -- Robert cannot overbid me for less than
18.05,
more than his reservation price.
Instead, we observe that many bidders delay bidding to the last minute
and
enter plural, escalating bids, rather than bidding the reservation price
and walking away. I've observed just two who bid once and never raise --
and I'm one of them (training effect).
Now, suppose I am absolutely rational but I believe that there are some
people who are not -- specifically who underbid their reservation
prices.
Then it may be rational for me, also, to underbid my reservation price.
Specifically: suppose Robert's reservation price for the item is 20.00,
and
mine is 17.55. However, Robert, supposing that he might get the item for
something less, has bid 10.00. If I come in with my 17.55 bid while he
has
time, Robert will overbid me; but if I wait until the last possible
minute,
and bid 10.50 with seconds to go while Robert has snoozed off, I get the
item for <ital>less than</ital> one tick over the second highest
reservation price.
I believe, however, that delayed and incremental bidding cannot be
"rational" for the potential winner, i.e. the bidder with the highest
reservation price. Had Robert bid his reservation price, he would have
gotten the item. Of course, there is the problem that the potential
winner
may not know, until late in the game, that he is the potential winner;
but
the fact remains that Robert has not played his best-response strategy.
Thus, under common knowledge of rationality -- if I know that everybody
else plays best-response -- my only rational strategy is to bid my
reservation price.
Experimental evidence indicates strongly that people are of different
"types" and not all (if any) are neoclassically rational.
Revised conjecture: Some bidders on Ebay are irrational types, and in
the
presence of irrational types, the rational behavior of others may be
quite
different than the common-knowledge-of-rationality Nash equilibrium.
Alternative conjecture (due to my wife, a collector of old salmon can
labels -- that's too long to explain -- ) These are really common value
auctions, or at least they have common-value elements. Many collectors
want
to assemble more or less complete sets of things, and a particular item
may
be more or less scarce, or even unique. If the bidder does not know how
rare the item is, incremental bidding makes sense. First, it may avoid
the
winner's curse -- which in this case means mis-estimating the scarcity
and
paying $90 in the belief that the item is rare, only then to see a dozen
of
them go for $30 each. Second, observing the bidding of others may convey
information about scarcity (especially when you know that two of the
bidders are maritime museum curators!)
Second alternative conjecture: Most often, people simply don't know what
their reservation prices are, since they do not have complete systems of
preferences over all possible goods and services. Instead, they have to
decide what their reservation prices are. Some do this consciously --
especially if they have been trained in economics. (I lean toward this
conjecture. I'm thinking somewhat carefully about an old news photograph
of
Huey Long even as I write). Others, however, do not, and experience
arousal
in the late stages of an auction that tends to increase their momentary
reservation prices, giving rise to incremental bidding even if they
always
bid their best estimate of their reservation price.
Of course, arousal has an entertainment value, too -- and one thing that
is
clear about EBAY is that it is (among other things?) in the
entertainment
business.
Roger A. McCain Professsor, Economics, Drexel University
mccainra@dunx1.ocs.drexel.edu 610-716-0044
http://william-king.www.drexel.edu/ origin code 33