We study the collective behaviour of a mixed population of minority game players (i.e. ``fundamentalists'') and majority game players (i.e. ``trend followers'' driven by imitation) by means of static and dynamical methods. When the fraction f of trend followers is smaller than 1/2, the system displays a transition from an ergodic, information-rich phase to a non-ergodic, unpredictable phase as the relative number of information patterns alpha is decreased. Here, trend followers essentially provide an additional signal that speculators can exploit. For f>1/2, instead, such a transition disappears and the global efficiency decreases steadily with alpha. Dynamical analysis is carried out via a path-integral technique, while the static calculus involves a non-standard (negative-dimensional) replica theory.