Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information

J. A. F. Heimel and A. C. C. Coolen

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Abstract: We study the dynamics of the batch minority game, with random external information, using generating functional techniques a la De Dominicis. The relevant control parameter in this model is the ratio $\alpha=p/N$ of the number $p$ of possible values for the external information over the number $N$ of trading agents. In the limit $N\to\infty$ we calculate the location $\alpha_c$ of the phase transition (signaling the onset of anomalous response), and solve the statics for $\alpha>\alpha_c$ exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For $\alpha

Date: 2000-12, Revised 2000-12
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Published in Phys. Rev. E 63, 056121 (2001)

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