Generating functional analysis of the dynamics of the batch minority game with random external information
Year: 2001
Type: article
Abstract: We study the dynamics of the batch minority game, with random external information, using generating functional techniques introduced by De Dominicis. The relevant control parameter in this model is the ratio $\ensuremath{\alpha}=p/N$ of the number p of possible values for the external information over the number N of trading agents. In the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ we calculate the location ${\ensuremath{\alpha}}_{c}$ of the phase transition (signaling the onset of anomalous response), and solve the statics for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$ exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$ the stationary state is shown to be nonunique. For $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\alpha}}}$0 we analyze our equations in leading order in \ensuremath{\alpha}, and find asymptotic solutions with diverging volatility $\ensuremath{\sigma}=O({\ensuremath{\alpha}}^{\ensuremath{-}1/2})$ (as regularly observed in simulations), but also asymptotic solutions with vanishing volatility $\ensuremath{\sigma}=O({\ensuremath{\alpha}}^{1/2}).$ The former, however, are shown to emerge only if the agents' initial strategy valuations are below a specific critical value.
Authors: J. A. F. Heimel, A. C. C. Coolen
Institution: King's College London
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2155545397