An Example of a Multi-agent System described as a Discrete Dynamical System

International audienceFinding adequate descriptions of multi-agent systems is a central issue for modelling collective dynamics. This article proposes a mathematical description of multi-agent systems as discrete dynamical systems. The ground of our proposition is the influence-reaction method of Ferber and M¨uller. The key idea is that agents should never act directly on other components of the system (agents or environment) but release influences which are then combined to update the state of the system. We propose a method which decomposes the definition of multi-agent system into six parts: (1) the basic sets, (2) the perception of the agents, (3) the influences, (4) the updating of the agents' internal state, (5) the updating of the environment, (6) the updating of the position and observable states of the agents. We illustrate our method on the multi- turmite model, also known as the multiple Langton's ants model. We then briefly discuss the relevance of this modelling method for the study of multi-agent systems