Shift operators and complex systems

In this paper, we deal with some multiagent systems modelling, based on population of automata. We focus our attention with automatic computation of emerging systems. A multiscale representation is proposed here and consists in representing the internal states of an agent behaviour by a automaton with multiplicities, on the one hand and an adaptive global system behaviour by a genetic algorithm over a population of automata, on the other hand. This genetic process can lead to generate many new automata which behaviour can be eventually similar. The role played by shift operators is to identify these similar behaviours. Two applications are presented. The first one concerns adaptive strategies in game theory. The second one concerns an automatic emerging computation of self-organised multiagent systems based on the efficience of operation expressivity of automata with multiplicities.