Agents, Equations and All That: On the Role of Agents in Understanding Complex Systems

Differential equations and agent-based models are different formalisms which can be applied to describe the evolution of complex systems. In this paper it is shown how differential equations can describe interactions among agents: it is pointed out that their capabilities are broader than it is often assumed, and it is argued that such an approach should be preferred whenever applicable. It is discussed under which circumstances it is however necessary to resort to agent-based models, and a rigorous approach is advocated in these cases. In particular, the relationship between the model and a theory of the processes under consideration provides both stimuli and constraints to the model. This relationship is discussed both in general terms and with reference to a specific example, which concerns a model of innovation processes.