2.2 Multiscale Structure of the Complex Multi-Agent Method

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According to the discussions above, Multi-Agent Paradigm concerns the study of complex systems for which the origin of complexity can be traced to the very attempt by our perception to describe a macroscopic number of “MICROscopic” objects and events in terms of a limited number of “MACROscopic” features .

Multi-Agent Modeling provides the techniques through which one can systematically follow the birth of the complex macroscopic phenomenology out of the simple elementary laws.

The Multi-Agent paradigm consists in deducing the macroscopic objects (Macros) and their phenomenological complex ad-hoc laws in terms of a multitude of elementary microscopic objects ( Micros) interacting by simple fundamental laws. The Macros and their laws emerge then naturally from the collective dynamics of the Micros as its effective global large scale features.

However, the mere microscopic representation of a system cannot lead to a satisfactory and complete understanding of the macroscopic phenomena. Indeed, the mere copying on the computer of a real-life system with all its problems does not by itself constitute a solution to those problems.

It is clear that a satisfactory Multi-Agent procedure of such complex systems has to be Multiscale.  Therefore, the Multi-Agent approach is not trying to substitute the study of one scale for the study of another scale; one is trying to unify into a coherent picture the complementary descriptions of a one and the same reality.

In fact one can have a multitude of scales such that the Macros of one scale become the Micros of the next level. As such the "elementary" Micros of one Multi-Agent Model do not need to be elementary in the fundamental sense: it is enough that the details of their internal structure and dynamics are irrelevant for the effective dynamics of the Macros.

More precise expressions of some of these ideas were encapsulated in the renormalization group and in the multigrid method.

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