Information Technology Reference
In-Depth Information
4. If the bid already contains quantities for 1, 2, and 3 above:
⎧
⎨
−
H
g
,
a
with probability .1
D
g
−
H
g
,
a
with probability .1
q
g
,
a
=
average between any two
consecutive (sorted) quantities
that are further apart
⎩
with probability .8
The method described gradually fills the largest gaps in the bid being constructed,
and “refreshes” each extreme occasionally with a 0.1 probability.
4.4
Results
The average performance relative to a global optimal allocation (i.e., assuming a cen-
tral planner) as calculated from our 58 trials is given in Table 3. Results show that AON
auctions quoting an anonymous full schedule provided the best performance, and that
AON auctions using either a standard or marginal unit quote performed worse than stan-
dard auctions with divisible bids. Using AON auctions with standard quotes provided
the worst average performance, although the differences with AON auctions quoting
marginal units are not statistically significant at reasonable levels.
Ta b l e 3 .
Results of 58 paired trials calculated as average performance in terms of global optimal.
Differences between 1 and 2 are significant at the 10
−
7
level, 2 and 3 at the .03 level, but 3 and 4
only at the 0.07 level.
# Auction
Quote
Average performance
1
AON
Full schedule
91.3 %
2 Standard
Standard
79.2%
3
AON
Marginal unit
70.7 %
4
AON
Standard
61.7%
We are not suggesting based on this particular experiment that the differences shown
in Table 3 are an indicator of the differences to be found under any possible parameter
configuration of our scenario or other settings. Before we ran the systematic paired
tests described above, we informally experimented with other parameter settings. Even
though we observed that AON auctions quoting full schedules always provided the best
average performance, in several settings the differences detected were not as stark.
4.5
Influence of Quoting
Quoting marginal prices with standard auctions makes sense from two perspectives.
First, it provides an accurate value for marginal units in order for agents to construct
their bids. Second, it provides a lower (upper) bound on both the unit price and total
payment to be paid (received) when bidding to buy (sell) an arbitrary number of units.
