This work aims to foster the interdisciplinary dialogue between
mathematicians and socio-economic scientists. Interaction among scholars
and practitioners traditionally coming from different research areas is
necessary more than ever in order to better understand many real-world
problems we face today. On the one hand, mathematicians need economists
and social scientists to better address the methodologies they design in
a more realistic way; on the other hand, economists and social
scientists need to be aware of sound mathematical modelling tools in
order to understand and, ultimately, solve the complex problems they
encounter in their research. With this goal in mind, this work is
designed to take into account a multidisciplinary approach that will
encourage the transfer of knowledge, ideas, and methodology from one
discipline to the other. In particular, the work has three main themes:
Demystifying and unravelling complex systems; Introducing models of
individual behaviours in the social and economic sciences; Modelling
socio-economic sciences as complex living systems. Specific tools
examined in the work include a recently developed modelling approach
using stochastic game theory within the framework of statistical
mechanics and progressing up to modeling Darwinian evolution. Special
attention is also devoted to social network theory as a fundamental
instrument for the understanding of socio-economic systems.