E ects of Regulation on a Self { Organized

Adapting a simple biological model, we study the eeects of control on the market. Companies are depicted as sites on a lattice and labelled by a tness parameter (somècompany{size' indicator). The chance of survival of a company on the market at any given time is related to its tness, its position on the lattice and on some particular external innuence, which may be considered to represent regulation from governments or central banks. The latter is rendered as a penalty for companies which show a very fast betterment in tness space. As a result, we nd that the introduction of regulation on the market contributes to lower the average tness of companies. Complex extended systems showing critical behavior, a lack of scale in their features, appear to be widespread in nature, being as diverse as earthquakes 1], river networks 2], and biological evolution 3]. The common characteristic of these systems is that they do not need any ne tuning of a parameter to be in a critical state. In an attempt to explain this behavior, Bak, Tang and Wiesenfeld introduced the concept of self{organized criticality (SOC) 4]. In the critical state, there are long range interactions, by which each part of the system feels the innuence of all the others. More precisely, this means that many of the relevant observables in the system follow a power{law or Pareto{L evy distribution with a non-trivial exponent.