Information Technology Reference
In-Depth Information
behaviour for any individual auction strongly depends on the auctions that are yet to be
conducted [7,3]. For example, consider sequential auctions for oil exploration rights.
In this scenario, the price an oil company will pay for a given area is affected not only
by the area that is available in the current round, but also by the areas that will become
available in subsequent rounds of leasing. Thus, it would be foolish for a bidder to spend
all the money set aside for exploration on the first round of leasing, if potentially even
more favourable sites are likely to be auctioned off subsequently.
Against this background, a key problem in the area is to study the strategic behaviour
of bidders in each individual auction. To date, considerable research effort has been
devoted to this problem, but an important shortcoming of existing work on sequential
auctions is that it focuses on objects that are either exclusively private value (different
bidders value the same object differently) or exclusively common value (an object is
worth the same to all bidders) [15,21,16,10,7]. Furthermore, some of this work also
makes the complete information assumption [16,2]. However, most auctions are neither
exclusively private nor common value, but involve an element of both [12]. Again,
consider the above example of auctioning oil-drilling rights. This is, in general, treated
as a common value auction. But private value differences may arise, for example, when
a superior technology enables one firm to exploit the rights better than others. Also, in
such cases, the common value (which is the same for all the bidders) depends on how
much each bidder values the object. Moreover, generally speaking an individual bidder
does not know the true common value, since it is unlikely to know how much the other
bidders value it. On the other hand, the private value of a bidder is independent of the
other bidders' private values.
Given this, our objective is to study sequential auctions for the general case where
there are both common and private value elements. We do this by modelling each ob-
ject with a two-dimensional signal: one for its common value and the other for its pri-
vate value component. Each bidder's information about the common value is uncertain .
Also, each bidder needs at most one object. The auctions are conducted using English
auction rules. For this model, we first determine equilibrium bidding strategies for each
auction in a sequence. On the basis of this equilibrium, we find the expected revenue
and the winner's expected profit for each auction. We show that even if the common and
private values are distributed identically across all objects, the revenue and the winner's
profit are not the same for all of them 1 . Specifically, we consider an example scenario
and show that in accordance with Ashenfelter's empirical result [1], the revenue for our
model can decline in later auctions.
Our paper therefore makes two important contributions to the state of the art in multi-
object auctions. First, we determine equilibrium bidding strategies for sequential auc-
tions that involve both common and private value elements. Second, we show that, in
accordance with Ashenfelter's experimental results [1], the revenue can decline in later
auctions.
1
This study is important because Ashenfelter [1] showed a declining price anomaly : in real-
world sequential auctions mean sale prices for identical objects decline in later auctions. In
contrast, for objects that are exclusively common/private value, the theoretical results of Mil-
grom and Weber [19,14], and McAfee and Vincent [13] show a completely opposite effect. Our
objective is therefore to show that, for our model, the revenue can decline in later auctions.
Search WWH ::




Custom Search