The mechanism for the self-adaptation behavior in the evolutionary minority game model

In this paper, we shall present our studies of a generalized evolutionary minority game model in which the agents are divided into several groups. The performance of the individual agent is averaged in each group. We find that there are three different effects in this generalized model, i.e. (1) group averaging effect, (2) left-right asymmetric effect, and (3) self-interaction effect. The former two effects favor the cautious agents, while the last one favors the extreme agents. In most cases, both the analytic results and the numerical simulations demonstrate that the group averaging effect is dominantly important and therefore the performance of the cautious agents is better than that of the extreme agents. However, when the number of groups is sufficiently large, the generalized model can be somehow reduced to the conventional evolutionary minority game model. As the parameters vary in the generalized model, the importance of the above three effects is exchangeable and different types of population distribution emerge.