Broken ergodicity and memory in the minority game
J. A. F. Heimel, A. De Martino
Abstract
We study the dynamics of the `batch' minority game with market-impact correction using generating functional techniques to carry out the quenched disorder average. We find that the assumption of weak long-term memory, which one usually makes in order to calculate ergodic stationary states, breaks down when the persistent autocorrelation becomes larger than cc=0.772... We show that this condition, remarkably, coincides with the AT-line found in an earlier static calculation. This result suggests a new scenario for ergodicity breaking in disordered systems.
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