Giulia Ajmone Marsan

Complex Systems and Society: Modeling and Simulation

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.

Modeling Cooperation and Competition in Socio-Economic Systems

This chapter shows how the mathematical tools derived in Chap. 2 can be profitably exploited for modeling social interaction dynamics. The focus is on cooperative and competitive games among the members of a social population, which result in a modification of the well-being of the individuals due to a redistribution of their global wealth. External actions related to welfare policies are also considered in the modeling approach.

Forward Look at Research Perspectives

This chapter presents some on research perspectives. Various topics are treated focusing on the following issues: further analysis of the modeling of welfare policy in the case of interactions in a network and in open systems; generalization of the modeling approach to various systems of social sciences, for instance opinion formation; modeling the interplay of different types of dynamics also viewed as a tool for predicting rare events; and analytic problems posed by the application of models to the study of social phenomena.

Welfare Policy: Applications and Simulations

This chapter is devoted to the investigation, through targeted numerical experiments, of various social scenarios predicted by the model presented in Chap. 3 in consequence of different simulated welfare policies. Qualitative simulations are developed with a mainly exploratory purpose, especially in order to test the ability of the model to account for the emergence of nontrivial collective average trends out of the probabilistic description of microscopic individual interactions. To this aim, a parameter sensitivity analysis is performed, which guides the organization of the simulations and the critical assessment of their results.

Mathematical Tools for Modeling Social Complex Systems

This chapter deals with the derivation of mathematical structures suitable for constructing models of phenomena of interest in social sciences. The reference framework is the approach of the Kinetic Theory for Active Particles (KTAP), which uses distribution functions over the microscopic states of the individuals composing the system under consideration. Modeling includes: the strategic behavior of active particles from a stochastic game perspective; a Darwinian-like evolution of the particles, which learn from past experience and evolve their strategy in time; and hints about small-network dynamics, in particular particle interactions within and among the nodes of the network. A critical analysis is finally proposed in order to assess the consistency of the mathematical tools with the main features of complexity.