The sigma profile: A formal tool to study organization and its evolution at multiple scales

Authors

  • Carlos Gershenson

    Corresponding author
    1. Computer Sciences Department, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México; New England Complex Systems Institute, Cambridge, Massachusetts 02142
    2. Centrum Leo Apostel, Vrije Universiteit Brussel, Krijgskundestraat 33, B-1160 Brussel, Belgium
    • Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad Universitaria, A.P. 20-726, 01000 México D.F. México
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Abstract

The σ profile is presented as a tool to analyze the organization of systems at different scales, and how this organization changes in time. Describing structures at different scales as goal-oriented agents, one can define σ ∈ [0,1] (satisfaction) as the degree to which the goals of each agent at each scale have been met. σ reflects the organization degree at that scale. The σ profile of a system shows the satisfaction at different scales, with the possibility to study their dependencies and evolution. It can also be used to extend game theoretic models. The description of a general tendency on the evolution of complexity and cooperation naturally follows from the σ profile. Experiments on a virtual ecosystem are used as illustration.

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