Information Technology Reference
In-Depth Information
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
10
0
10
1
10
2
10
−1
10
0
10
1
N/
2
m
(
Ns
)
/
2
m
Fig. 2.
Left: Comparison of correctness
Ψ
for the minority and majority games for
S
= 2 and variable
N
. Red dashed line corresponds to the minority game and green
solid line to the majority game. Right: Solid grey line corresponds to the theoretical
maximal value, green dotted line corresponds to MG for
N
= 1 and various
S
values,
blue dashed line corresponds to MG for
S
= 5 and various
N
values, red dash-dotted
line corresponds to MG for
S
= 2 and various
N
values. The 'x' mark corresponds
to MG for
N
=1and
S
= 16 pairwise different strategies from the RSS.The star '*'
corresponds to MG for
N
=1and
S
= 256 pairwise different strategies from the FSS.
If the order is unknown but the type of the process is known (e.g. autoregres-
sive one) some techniques based on the autocorrelation analysis can be applied
to detect the order, as presented in Ref. [1].
The problem is most dicult if the order and the system are unknown, as it is
in many real cases (e.g. prices in financial markets). Still the correlation analysis
can suggest the number of past samples be used. In this section we assume that
the order of the examined AR process is explicitly given.
In order to find the proper technique for
N
and
S
optimization, let us assume
that a certain pool of strategies of constant size has to be optimally assigned to
agents. It means that, under the constraint
NS
=
const
, we are looking for the
proportion between number of agents
N
and number of strategies per agent
S
that maximizes the correctness
Ψ
. We would also like to examine if the optimal
proportion is sensitive to the constraint's change. Our numerical studies are
presented in Fig. 2. The correctness is presented as a function of
NS
, as changing
the size of the strategies' pool influences the results. Solid grey line corresponds
to the maximal value that is reached by the best possible predictor (in this case
linear filter). Blue dashed line corresponds to MG for
S
= 5 and various
N
values,
red dash-dotted line corresponds to MG for
S
= 2 and various
N
values. These
two curves show that the more strategies per agent the better the correctness
Ψ
, provided that the constraint
NS
=
const
is preserved. Following further this
reasoning, the most ecient is obtained for just one agent possessing given pool
of strategies. Indeed, this is confirmed by the green dotted line corresponding
to MG for
N
= 1 and various
S
values. As it is seen, the predictor with such
configuration outperforms any other predictor.
