Dynamics of the batch minority game with inhomogeneous decision noise.
Phys Rev E Stat Nonlin Soft Matter Phys 65:1 Pt 2 (2002) 016126
Abstract:
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio alpha=p/N of the number p of possible values for the external information over the number N of trading agents, and the statistical properties of the agents' decision noise parameters. The presence of decision noise is found to have the general effect of damping macroscopic oscillations, which explains why in certain parameter regions it can effectively reduce the market volatility, as observed in earlier studies. In the limit N-->infinity we (i) solve the first few time steps of the dynamics (for any alpha), (ii) calculate the location alpha(c) of the phase transition (signaling the onset of anomalous response), and (iii) solve the statics for alpha>alpha(c). We find that alpha(c) is not sensitive to additive decision noise, but we arrive at nontrivial phase diagrams in the case of multiplicative noise. Our theoretical results find excellent confirmation in numerical simulations.Coupled dynamics of sequence selection and compactification in mean-field hetero-polymers
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 35:41 (2002) PII S0305-4470(02)38407-5
Statistical physics of induced correlation in a simple market
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 311:3-4 (2002) PII S0378-4371(02)00835-X
Glassy behaviour in a 3-state spin model
Journal of Physics A: Mathematical and General 34:25 (2001) 5147-5182