Complexity and economy

Complex systems are a research field extraordinarily charming: they are universally popular, not only in physics and chemistry, but also in biology, in economics and social sciences. The science of complexity also deals with domains that have long frustrated attempts to quantitative description rigorous: for example in economy are undergoing a major developments related to the possibility of simulating the interaction between agents that are modeled in such a way as to renounce to the unrealistic assumption of the classical economy, as for example that of behavior perfectly rational. The main characteristics that were associated with the complexity relate to the presence of numerous elements interacting, the non-linearity of the interactions, the appearance in the overall level of emerging properties without a microscopic analogue, and last but not least the ability of self-organization. Each of these aspects deserves to be deepened, but it should be noted that a characteristic common to the systems that we consider complex is the ability to amplify a small local phenomenon bringing all the system in a state qualitatively new. Consider for example a phase transition as that from water to ice, which occurs (at temperatures below the freezing point) when local fluctuations give rise to a solid region large enough that the gain in free energy, associated with the formation of the solid phase, exceeds the energy cost relative to the formation of an interface between the two phases: this region is therefore stable and acts as a nucleus of condensation for further accretions, while a similar solid region, smaller size would be condemned to death