Kinetic modelling of complex socio-economic systems

Abstract

This chapter is devoted to the investigation of the complex mechanisms which rule the transition from the behavior of single individuals to the collective behavior of groups of people, in social phenomena. The dynamics of our societies are ruled by many complex socio-economic phenomena, which still lack a proper support of robust mathematical models. A deeper understanding can possibly lead to important improvements in the explanation of various events of our times. By means of the kinetic theory of active particles (KTAP), a mathematical framework suitable to model complex socio-economic systems is derived. This framework is based on concepts already introduced in [1-3]. Once the mathematical framework has been established, the second part of the chapter focuses on one specific application: the spread of opinions in a multi-community population affected by media. Different individuals belonging to different groups dynamically interact according to rules that take into account their social state and condition. We show which distributions of social groups in the global population emerge, and how these distributions change according to some key parameters of the model.