Theory of the Three-Group Evolutionary Minority Game

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.