In recent years, the models and methodologies typically adopted in physics
have proven useful for studying various social phenomena. In this thesis, we
borrow concepts from physics to explore different models of highly complex
social systems. In constructing these models, we aim to capture general insights
through statistical mechanics and probability theory while keeping them simple
and intuitive. The ultimate goal is not to fully understand the examined social
phenomena, a challenging or even impossible task, but rather to provide a
starting point and inspiration for future research.
We begin this thesis with a brief introduction to social physics in Chapter 1.
Specifically, we introduce the basic concepts of complex systems, such as
social systems. We then provide a historical overview of the emergence of
sociophysics and discuss, through subjective considerations, the potential,
limitations, and future objectives that physicists approaching social sciences
should strive for. In the following two chapters, we study different models of
social interaction: dyadic interaction and interaction within groups. In
particular, in Chapter 2, we examine the pairwise matching problem from a
different perspective. While traditional matching theory considers rational
agents with complete information, we study a more realistic version where
individuals have only local information and self-organize to achieve a final
matching that demonstrates properties different from classical matching
problem solutions. Using a similar methodology, we propose a simple
negotiation model between two individuals. In Chapter 3, we address the
problem of community and group formation. First, we show analytically
interesting properties of the clustering coefficient in social networks with a
simple yet non-trivial model. We then introduce a group formation model to
study how different mechanisms for selecting new members influence the
cohesion and stability of the group. In Chapter 4, instead, we dive into the
topical problem of opinion formation. We investigate the mechanisms through
which individuals, independently of social influence, decide to believe certain
sources of information over others, considering their limited computational
capabilities. Finally, in Chapter 5, we provide a broader view of this thesis and social physics in general.