Information Technology Reference
In-Depth Information
4.3
Selection of New Bidding Points
In each iteration
a
of the main loop, an agent updates its bid for good in auction
g
with one new point (
p
g
,
a
,
q
g
,
a
), taking into account current holdings and assuming other
goods (not in auction
g
) could be freely bought or sold at the most recent quote. We used
two different methods for picking incremental points, one for dealing with divisible bids
and another for indivisible ones.
DIVISIBLE: For divisible bids, an agent selects a new bidding point for the good in
auction
g
by picking a price
p
g
,
a
and calculating the quantity
q
g
,
a
the agent would be
willing to buy or sell at such price in order to maximize its profit. Calculation is done
using an ILP model that encodes the agent's utility function as explained in Section 3.2.
Prices
p
g
,
a
are selected in the following arbitrary order:
1.
p
g
,
a
=
BID
2.
p
g
,
a
=
ASK
3. If the bid in
g
already contains prices for 1 and 2 above,
p
g
,
a
is selected from a
normal distribution
N
(
μ
,
1),
⎧
⎨
(
hb
+
ASK
)
/
2
if
q
a
−
1
>
0
∨
(
q
a
−
1
= 0
∧
pr
<.
25)
(
ls
+
BID
)
/
2
if
q
a
−
1
<
0
∨
(
q
a
−
1
= 0
∧
pr
<.
5)
μ
=
⎩
lb
if (
q
a
−
1
= 0
∧
pr
<.
75)
hs
otherwise
where
hb
(
hs
)and
lb
(
ls
) are the highest buy (sell) and lowest buy (sell) offers
already in the bid and
pr
is a random value uniformly distributed between 0 and 1.
(Note that
BID
and
ASK
refer to the most recent quote obtained by the agent.)
The basic idea behind the approach described above is to help agents find feasible
trades by gradually making them place their highest buy and their lowest sell offer.
We empirically tested other alternatives to ensure that our comparison of divisible ver-
sus indivisible bidding was not biased by an unreasonable point-selection approach.
Specifically, we compared the procedure described with a random selection of points,
and also with another in which prices are picked by finding the maximum possible gap
between any two consecutive pairs of (sorted) prices already in the bid and selecting
their average. Our results indicated that the approach chosen provided the best average
performance among the alternatives we evaluated.
INDIVISIBLE: For indivisible bidding, the agent selects a new bidding point for
the good in auction
g
by picking a quantity
q
g
,
a
. The payment
p
g
,
a
is given by the
maximum (minimum) value at which the agent is willing to buy (sell)
q
g
,
a
units, which
is calculated using an ILP model that encodes the agent's utility function as explained
in Section 3.2. Quantities
q
g
,
a
are selected in the following order:
1.
q
g
,
a
=
H
g
,
a
(sell all holdings available in iteration
a
)
2.
q
g
,
a
=
D
g
−
−
H
g
,
a
(buy all available items, i.e., demand minus holdings)
3.
q
g
,
a
= random value uniformly distributed in the range [
−
H
g
,
a
,
D
g
−
H
g
,
a
] (exclud-
ing 0)
