Information Technology Reference
In-Depth Information
3
Off-Line Analysis of Data
The first step in our approach is to identify and characterize market regimes by ana-
lyzing off-line data from previous games. The agent will use these results along with
real-time observable information to identify regimes during the game, forecast regime
transitions, and adapt its procurement, production, and pricing strategy accordingly.
For our experiments, we used data from a set of 26 games played during the semi-
finals and finals of TAC SCM 2004. The number of games played was 30, but we left out
the games where some computers were sold for $0. The mix of players changed from
game to game, the total number of players was 12 in the semi-finals and 6 in the finals.
x 10
4
2
2
6
Product Quantity
p(np)
p(np|c
1
)*P(c
1
)
p(np|c
2
)*P(c
2
)
p(np|c
3
)*P(c
3
)
1.5
4
1
2
0.5
0
0
0
0
0
0
0.2
0.2
0.2
0.4
0.4
0.4
0.6
0.6
0.6
0.8
0.8
0.8
1
1
1
1.2
1.2
1.2
Normalized Price (np)
Fig. 2.
The Gaussian mixture model for the low market segment. Data are from 26 games from
finals and semi-finals of TAC SCM 2004.
Each computer type has a different nominal price, which is the sum of the nominal
cost of each of the parts needed to build it. We normalize the prices across the different
computer types in each market segment. We call np the normalized price.
We define regimes with the help of a Gaussian mixture model (GMM). We apply the
EM-Algorithm [2] to determine the Gaussian components of the GMM,
N
[
μ
i
,σ
i
](np),
and their prior probability,
P
(
c
i
). The density of the normalized price can be written as:
N
p
(np) =
p
(np
|
c
i
)
P
(
c
i
)
(1)
i
=1
where
p
(np
c
i
) is the
i
-th Gaussian from the GMM. An example of the Gaussians is
shown in Figure 2. For our experiments we chose
N
=3, because we found experimen-
tally that this provides a good balance between quality of approximation and simplicity
of processing.
|
