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agents are homogeneous, except in their bidding strategies, to facilitate analysis
of the results.
The Auctions =
are held sequentially. In
each auction i one separate load l is sold. We let each auction i be a Vickrey second
price auction. This choice is motivated by three reasons. First of all, Vickrey
auctions have limited overhead in communication and are straightforward to
handle by the auctioneer. Second, for the last known auction auction t , or for an
auction that if won fills the agent to capacity, the agents, as derived from auction
theory under some mild conditions, have as dominant strategy to bid their true
valuation. Thirdly, use of Vickrey auctions gives a basis for a simple bidding
strategy to formulate baseline agents to compete against in the computational
experiments. These baseline agents, which we call myopic bidders, in each auction
simply bid their true valuation for the item for auction (if not full) as if there
were no future auctions to be taken into consideration.
We note that the results of Section 4 and the analysis of Section 5 are not
dependent on the specific choice of auction. We feel a first price, sealed bid
auction will result in comparable equilibrium outcomes. However, the additional
strategic deliberations available in an open cry auction, i.e. each agent knows
the going price (and the winner), can allow an agent to more quickly adapt and
arrive at our predicted equilibrium outcomes.
The loads for auction originate in fruitful regions [9] where FruitfulRegions =
{
auction 1 ,auction 2 ,...,auction t }
{
. Each fruitful region represents a cluster of customers that re-
quire transport of loads to a central depot D . The fruitful regions are differ-
entiated in the number of loads they offer in one sequence of auctions and are
abstract representations of populations.
F 1 ,F 2 ,...,F n }
4
20
(2,0)
F
1
1
F
(1,0)
2
0.5
0.5
5
(0,0)
(1,1)
F
3
0.5
0.5
(0,1)
1
D
(0,2)
Fig. 1. Fruitful regions (a) and state representations (b)
In Figure 1a, there are three fruitful regions F 1 , F 2 ,and F 3 from which loads
originate that have to be delivered to the depot D . An agent can, for example,
pick up 2 loads in region F 2 and continue to region F 3 and pick up one more
before returning to the depot D .
An agent j
Agents has a private valuation function for an auctioned load l .
In Figure 1a, the valuation is influenced by the already won loads L in previous
auctions, as movement cost is a major factor in calculating the marginal utility of
accepting a new load l for transport. For example, the agent above for Figure 1a
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