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Grand Canonical Minority Game
as a Sign Predictor
Karol Wawrzyniak and Wojciech Wislicki
National Centre for Nuclear Research
Hoza 69, 00-681 Warszawa, Poland
{
kwawrzyn,wislicki
}
@fuw.edu.pl
Abstract.
In this paper the extended model of Minority game (MG), in-
corporating variable number of agents and therefore called Grand Canon-
ical, is used for prediction. We proved that the best MG-based predictor
is constituted by a tremendously degenerated system, when only one
agent is involved. The prediction is the most e
cient if the agent is
equipped with all strategies from the Full Strategy Space. Despite the
casual simplicity of the method its usefulness is invaluable in many cases
including real problems. The significant power of the method lies in its
ability to fast adaptation if
λ
-GCMG modification is used. The success
rate of prediction is sensitive to the properly set memory length. We
considered the feasibility of prediction for the Minority and Majority
games.
Keywords:
Minority Game as a predictor, Financial Markets.
1
Introduction
The minority decision is defined as a function of a self-generated signal called ag-
gregate attendance or aggregate demand [4] (Sec. 2). The MG can be potentially
used as the predictor of any exogenous (fake) series, provided that dependencies
in the signal reflect the patterns built in strategies[11,8,9]. The details of the
current state of the art are presented further in Sec. 3. In Sec. 4 we presented
the model and its configuration. Then, in section 5, we verified the quality of the
predictor using the time series generated by the well understood, autoregressive
stochastic process. After analyzing our numerical results, we provided a method-
ology for tuning the parameters. Intriguingly, the best results are achieved if the
game is degenerated to only one single agent equipped with all strategies from
the whole strategy space. This new discovery seems to stay in contradiction to
commonly used optimization techniques [11,8,9]. Additionally, in Sec. 5 we pre-
sented some new insights which allow us to improve the model. For example, it
was proved that if the exogenous signal is exploited, then there is no qualitative
difference between minority and majority game. We also introduced a modifi-
cation, the so called
λ
-GCMG, that is well suited for quasti-stationary signals.
Finally, in the Sec. 5, the properly tuned MG model was applied as a forecaster
of assets prices on financial markets.
