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

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  • J. A. F. Heimel
  • A. C. C. Coolen

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

Suggested Citation

  • J. A. F. Heimel & A. C. C. Coolen, 2000. "Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information," Papers cond-mat/0012045, arXiv.org, revised Dec 2000.
    • Handle: RePEc:arx:papers:cond-mat/0012045
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