Information Technology Reference
In-Depth Information
0.9
m=9, n=20
m=9, n=19
m=9, n=18
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
1
2
3
4
5
6
7
8
9
Auction
Fig. 5.
The winner's expected profit for a varying competition
for different
n
. As seen in the figure, for all the three values of
n
, the winner's expected
profit also decreases from one auction to the next.
5
Related Work
Existing work has studied the dynamics of the revenue of objects for sequential auc-
tions [15,19,14,3]. However, a key limitation of this work is that it focuses on objects
that are either exclusively private value or exclusively common value. For instance,
Ortega-Reichert [15] determined the equilibrium for sequential auctions for two private
value objects using the first price rules. Weber [19] showed that in sequential auctions
of identical objects with risk neutral bidders who hold independent private values, the
expected revenue is the same for each auction. On the other hand, Milgrom and Weber
[14] studied sequential auctions in an interdependent values model with affiliated
5
sig-
nals. They showed that expected revenues have a tendency to drift upward. This may
be because earlier auctions release information about the values of objects and thereby
reduce the winner's curse problem.
In contrast to the above theoretical results, there has been some evidence in real-
world sequential auctions for identical objects - for art and wine auctions in particular -
that the prices tend to drift downward [1,13]. Because the theoretical models mentioned
above predict either a stochastically constant or increasing price, this fact has been
called the
declining price anomaly
. Mc Afee and Vincent [13] consider two identical
private value objects and using the second price sealed bid rules, they show that the
declining price anomaly cannot be explained even if the bidders are considered to be
risk averse. Bernhardt and Scoones [3] show a decline in the sale price by considering
two private value objects. Here, we generalise this model to
n>
2 objects with both
common and private values
6
. Although the objects we consider have both common and
5
Affiliation is a form of positive correlation. Let
X
1
,
X
2
, ...,
X
n
be a set of positively corre-
lated random variables. Positive correlation roughly means that if a subset of
X
i
sarelarge,
then this makes it more likely that the remaining
X
j
s are also large.
6
Multi-object auctions for common and private value objects have been studeied in [8]. This
work focusses on the efficiency of these auctions, while our present work focusses on the
variation in the revenue of such auctions.
