Broken ergodicity and memory in the minority game

Details Broken ergodicity and memory in the minority game Broken ergodicity and memory in the minority game

2001-08-03

arxiv.org/abs/cond-mat/0108066v2

J.Phys.A 34 (2001) L539-L545

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 3 figures, final version. To appear in J.Phys.A

Scientific paper

10.1088/0305-4470/34/40/103

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 c_c=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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