Stochastic decision-making in the minority game

A discussion is presented of the effects of stochasticity in the decision-making of agents in the minority game. Both simulational and analytic results are reported and discussed for both additive and multiplicative noise. As a function of the ratio d of information dimension to number of agents a phase transition separates a low d non-ergodic phase from a high d ergodic phase. For additive noise the critical d, is temperature-independent but for multiplicative noise d(c) (T) decreases with T. Additive noise does not affect the asymptotic behaviour for d > d(c) but is relevant below d(c). Multiplicative noise has consequence for all d. (C) 2002 Elsevier Science B.V. All rights reserved