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An Analysis of Sequential Auctions
for Common and Private Value Objects
Shaheen S. Fatima 1 , Michael Wooldridge 1 , and Nicholas R. Jennings 2
1 Department of Computer Science,
University of Liverpool, Liverpool L69 7ZF, U.K.
{ S.S.Fatima, M.J.Wooldridge } @csc.liv.ac.uk
2 School of Electronics and Computer Science,
University of Southampton, Southampton SO17 1BJ, U.K.
nrj@ecs.soton.ac.uk
Abstract. Sequential auctions are an important mechanism for buying/selling
multiple objects. Now existing work in the area has studied sequential auctions
for objects that are exclusively either common value or private value. However,
in many real-world cases an object has both features. Also, in such cases, the
common value depends on how much each bidder values the object. Moreover, a
bidder generally does not know the true common value (since it may not know
how much the other bidders value it). Given this, our objective is to study set-
tings that have both common and private value elements by treating each bidder's
information about the common value as uncertain . Each object is modelled with
two signals: one for its common value and the other for its private value. The
auctions are conducted using English auction rules. For this model, we first de-
termine 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 then show that even if the common and private values
of objects are distributed identically across all objects, the revenue and the win-
ner's profit are not the same for all of them. We show that, in accordance with
Ashenfelter's experimental results [1], the revenue for our model can decline in
later auctions.
1
Introduction
Market-based mechanisms such as auctions are now being widely studied as a means
of buying/selling resources in multiagent systems. This uptake is occurring because
auctions are both simple and have a number of desirable properties (typically the most
important of which are their ability to generate high revenues to the seller and to allo-
cate resources efficiently) [18,4,20]. Now, in many cases the number of objects to be
auctioned is greater than one. There are two types of auctions that are used for multiple
objects: combinatorial auctions [17] and sequential auctions [7,3,11]. The former are
used when the objects for sale are available at the same time, while the latter (which
are the main focus of this paper) are used when the objects become available at differ-
ent points in time. In the sequential case, the auctions are conducted at different times,
therefore a bidder may participate in more than one auction. In such a scenario, it has
been shown that although there is only one object being auctioned at a time, the bidding
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