  Based on the adiabatic theory for the evolutionary minority game (EMG) that
we proposed earlier[1], we perform a detail analysis of the EMG limited to
three groups of agents. We derive a formula for the critical point of the
transition from segregation (into opposing groups) to clustering (towards
cautious behaviors). Particular to the three-group EMG, the strategy switching
in the "extreme" group does not occur at every losing step and is strongly
intermittent. This leads to an correction to the critical value of the number
of agents at the transition, $N_c$. Our expression for $N_c$ is in agreement
with the results obtained from our numerical simulations.
