Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2005-08-18
J. Stat. Mech. (2005) P10009
Physics
Condensed Matter
Disordered Systems and Neural Networks
26 pages, 8 figures; typo corrected
Scientific paper
10.1088/1742-5468/2005/10/P10009
Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary state on initial conditions. The model thus bears more similarity with the original MG. Still, all order parameters including the volatility can computed in the ergodic phases without making any approximations. We also study the effects of market impact correction on the phase diagram. Finally we discuss a continuous-time version of the model as well as the differences between on-line and batch update rules. Our analytical results are confirmed convincingly by comparison with numerical simulations. In an appendix we extend the analysis of the earlier spherical MG to a model with general time-step, and compare the dynamics and statics of the two spherical models.
Galla Tobias
Sherrington David
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