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Repeated Auctions with Complementarities
P.J. 't Hoen 1 and J.A. La Poutre 2
1 Center for Mathematics and Computer Science (CWI)
P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Phone: +31 20 5929333; Fax: +31 20 5924199
2 TU Eindhoven
De Lismortel 2, 5600 MB Eindhoven, The Netherlands
{ hoen, hlp } @cwi.nl
Abstract. There is an extensive body of literature concerning optimal
bidding strategies for agents participating in single shot auctions for
single, individually valued goods. However, it remains a largely open
question how a bidder should formulate his bidding strategy when there
is a sequence of auctions and, furthermore, there are complementarities
in the valuation for the bundle of items acquired in the separate auctions.
We investigate conditions for which adjusting the bidding horizon beyond
the immediate auction is profitable for a bidder. We show how such a
strategy, in the limit, reduces agents to zero marginal profits as predicted
by the Bertrand economic theory. We support our experimental results
by drawing a parallel to the nIPD.
1
Introduction
With the rapid growth of agent-mediated electronic commerce, it is becoming
increasingly evident that in a few years the Internet will host large numbers
of interacting software agents instead of human bidders and auctioneers. The
large-scale application of software agents is becoming inevitable due to the in-
creasing number, complexity, and interactions between available online auctions.
In line with this development, there is a growing body of literature on market-
based allocation of scarce resources in competitive Multi-Agent Systems (MASs)
[2,12,14], where the focus in the research is on sophisticated auction mechanisms
and bidding strategies grounded in auction theory [10].
The field of auction theory has intensively explored optimal bidding strategies
for single shot auctions, i.e. auctions for individual items. For example, it is well
known that the dominant strategy in the second price Vickrey auction [16] for
an agent is to bid its true valuation of a good. This property, however, does not
carry over in the case of future auctions when, for example, there are substitute
goods expected in future auctions. An agent then needs to deliberate the possi-
ble value of waiting for a future, possibly cheaper auction. The formulation of a
good bidding strategy is even more complex when a bundle of goods is desired,
as illustrated in [8] and [15] for the TAC classic 1 . As another example, consider
1 Visit http://www.sics.se/tac for details.
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