Modeling And Simulating Hierarchies Using An Agent-Based Approach

The notion of complex system covers many different meanings. Socio-economical and ecological systems are typically kind of 'organized complex systems', defined as a middle number of heterogeneous components interacting in an intricate manner and producing emergent properties and dynamics. The only possibility to understand and to model such complex systems is to exhibit some organizational principles behind the apparent inextricability. The hierarchy theory in ecology allows a decomposition of this kind of systems that could improve our understanding of the underlying dynamic processes. Formally, it is a view of ecological systems, which takes the scales of observation explicitly into account and which tries to conceptualize the phenomena at their proper scale. This conceptualization mostly exhibits nested hierarchical systems in the sense that a system at a given scale contains its component subsystems at the underlying scale. Socio-economical systems additionally exhibit non-nested hierarchies in which representatives of social groups (and not the groups themselves) form higher level groups or organizations. The aim of this paper is to propose a set of concepts to formalize both nested and non-nested hierarchical systems. For the first kind of systems, we will review the hierarchy theory in ecology to extract the main concepts, mainly the concept of holon. Independently, we will review the concepts of agents, groups and roles (AGR) to represent eco-sociological systems as proposed in Ferber et Gutknecht (1998). Finally, we will propose a modeling and simulation formalism able to represent these concepts in a unified framework and discuss some of its advantages and disadvantages.