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(the nature, variance, and the neighborhood) defines the regime. A regime captures a
somewhat medium term mood in the market by looking at price and volume tradeoffs.
A price point does not consider its neighborhood, an idea that regimes capture.
4
Online Identification of Current Regime
During the game, the agent can estimate every day the current regime by calculating
the mean normalized price np
day
for the day and by selecting the regime which has the
highest probability, i.e. argmax
1
≤k≤M
P
(
R
k
|
np
day
)
.
1.2
1
0.8
0.6
0.4
Maximum Price
Mean Price
Minimum Price
0.2
0
0
20
40
60
80
100
120
140
160
180
200
220
Time in Days
Fig. 5.
Game 1189@tac4 (Final TAC SCM 04) - Minimum and maximum daily prices of com-
puters sold, as reported during the game every day, and mean price. If nothing was sold in the
market on a given day then the prices shown are below zero. The mean price is computed after
the game using the game data, which include complete information on all the transactions.
Unfortunately, this is not simple, since the agent has only limited market information
during the game. Every day the agent receives a report which includes the minimum
and maximum prices of the computers sold the day before, but not the quantities sold.
Using these reports, the agent can compute the mid-range of the normalized price of the
computers sold the previous day. The mid-range is an estimate of the mean price, but
not always a good one since the quantity of computers sold is not known. An example
that shows how the mean differs from the mid-range value is shown in Figure 5.
The mid-range price can be used to identify the corresponding regime online, as
shown in Figure 6 (left). The data are from game 1189@tac4, which was not in the
training set of games used to develop the regime definitions. The middle and right parts
of Figure 6 show respectively the probability of receiving an order in a balanced and in
a scarcity situation for different prices. Scarcity typically occurs early in the game and
