Continuous time dynamics of the thermal minority game

We study the continuous time dynamics of the thermal minority game. We find that the dynamical equations of the model reduce to a set of stochastic di fferential equations for an interacting disordered system with nontrivial r andom diffusion. This is the simplest microscopic description which account s for all the features of the system. Within this framework, we study the p hase structure of the model and find that its macroscopic properties strong ly depend on the initial conditions.