Dear Guys, J'ai juste corrigé l'anglais. Je reprendrai le tout plus tard. G. %%%%%%%%%%%%%%%%%%%%%%%%%% In this paper, we deal with some multi-agent systems modeling, based on population of automata. We focus our attention with automatic computation of emerging systems. A multi-scale representation is proposed here and consists in representing the internal states of an agent behavior by a automaton with multiplicities, on the one hand, and an adaptive global system behavior by a genetic algorithm over a population of automata, on the other hand. This genetic process can lead to generate many new automata which behavior can be eventually similar. The role played by shift operators is to identify these similar behaviors . Two applications are presented. The first one concerns adaptive strategies in game theory. The second one concerns an automatic emerging computation of self-organized multi-agent systems based on the efficience of operation expressivity of automata with multiplicities. %%%%%%%%%%%%%%%%%%%%%%%%%%