Broken ergodicity and memory in the minority game
Disordered Systems and Neural Networks
2009-11-07 v2 Trading and Market Microstructure
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 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.
Keywords
Cite
@article{arxiv.cond-mat/0108066,
title = {Broken ergodicity and memory in the minority game},
author = {J. A. F. Heimel and A. De Martino},
journal= {arXiv preprint arXiv:cond-mat/0108066},
year = {2009}
}
Comments
6 pages, 3 figures, final version. To appear in J.Phys.A