Complexity: from natural to socio-economic sciences: - Introductory Concepts - Complexity of Countries and Products - Agent Based Models in Economics

We discuss how complexity ideas can have an important impact in socio-economic disciplines with two examples. The critics to the standard model of economics suggest the introduction of concepts like finite rationality and strong interactions among agents, intrinsic instabilities and self-organized critical states which are typical of complexity models. On the other hand the strong fluctuations of the number of agents implies new ideas which are not contained in the physical models. We describe the state of the art of the Agent Based Models and outline the possible developments and their implications for the problem of systemic risk. We also discuss a recent new approach to the complexity of countries and products in the spirit of the recent papers by Hidalgo and Hausmann. The basic idea is that the use of statistical concepts inspired to the page rank (Google) problem may lead to a novel classification for the fitness of the countries and the quality of products which adds new information with respect to the standard economic analysis.