  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
differential equations for an interacting disordered system with non-trivial
random diffusion. This is the simplest microscopic description which accounts
for all the features of the system. Within this framework, we study the phase
structure of the model and find that its macroscopic properties strongly depend
on the initial conditions.
