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 dc is temperature-independent but for multiplicative noise dc(T) decreases with T. Additive noise does not affect the asymptotic behaviour for d>dc but is relevant below dc. Multiplicative noise has consequence for all d.