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a software agent shopping for the cheapest possible computer assembled from
parts. An incomplete bundle has a large negative impact on utility. The litera-
ture investigates two main solutions; simultaneous auctions and combinatorial
auctions.
The first solution proposes for agents to participate in parallel auctions, one
for each desired item in the bundle [6]. This however is problematical as an agent
can have an exposure problem, i.e. how much of a sunk cost is incurred if one or
more items of the bundle are not won. This exposure problem is not evident for
combinatorial auctions, where the burden has shifted from estimating the value
of individual goods to bidding on and estimating the value of complete bundles
[14]. Both type of auctions however require availability (or at least knowledge)
of all goods for auction at the same time.
This last issue of availability can be infeasible in practice. For example, an
agent may have to procure a bundle of items where the items are auctioned
at different points in time. Consider also a logistics setting where orders for
transport are auctioned online. New opportunities for transport dynamically
occur in the course of operations as clients place new orders. It is then an issue as
to how well a new order can fit into an existing schedule, as this is a determining
cost factor. For example, an agent that is better able to expect future demand
has a better bundling of drop off points for cargo and is able to make a higher
profit due to a more ecient route.
A characteristic of the above examples is that agents have to incorporate in
their bidding strategy an expectation of emerging future items, expected compe-
tition, and an estimate of the complementary 2 value of possible items in auctions
still to come. Goods with complementarities are items whose value as a bundle
is higher than the value of the items considered in isolation. The search for a
good bidding strategy for bundles with complementary issues in the items for
such a repeated auction setting is still largely an open question, but a growing
and essential area of research [5]. Much of this research has been restricted to a
limited number of agents, bundles, number of items in the bundles, known order
of the auctions, or to specific scenarios.
We extend the previous work by analyzing agents competing for a large num-
ber of unknown, individual items still to be auctioned to form profitable bundles.
More specifically, we study a set of agents based on a logistics domain. This do-
main is of interest due to its large-scale application, its competitive nature, and
its dynamic setting. These aspects make it a representative setting for evaluating
bidding strategies.
The capacitated agents compete for orders by bidding for available cargo as
these are offered in consecutive auctions. Each agent, in the face of competition,
has to learn to focus on types of bundles, depending on already won orders, in
order to maximize expected profit in auctions still to come. We show, using com-
putational experiments, that individual agents have an incentive to bid higher
(overbid) than the immediate valuation of a good if this increases probability of
2 This in the literature is also called super-additive or synergy[11], i.e. u ( {A, B} ) >
u ( {A} )+ u ( {B} ).
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