Models of Society and Complex Systems
Models of Society and Complex Systems introduces readers to a variety of different mathematical tools used for modelling human behaviour and interactions, and the complex social dynamics that drive institutions, conflict, and coordination. What laws govern human affairs? How can we make sense of the complexity of societies and how do individual actions, characteristics, and beliefs interact? Social systems follow regularities which allow us to answer these questions using different mathematical approaches.
This book emphasises both theory and application. It systematically introduces mathematical approaches, such as evolutionary and spatial game theory, social network analysis, agent-based modelling, and chaos theory. It provides readers with the necessary theoretical background of each toolset as well as the underlying intuition, while each chapter includes exercises and applications to real-world phenomena. By looking behind the surface of various social occurrences, the reader uncovers the reasons why social systems exhibit both cultural universals and at the same time a diversity of practices and norms to a degree that even surpasses biological variety, or why some riots turn into revolutions while others do not even make it into the news.
This book is written for any scholar in the social sciences interested in studying and understanding human behaviour, social dynamics, and the complex systems of society. It does not expect readers to have a particular background apart from some elementary knowledge and affinity for mathematics.
1. Introduction 2. Game Theory: Strategic Interactions 3. Evolutionary Game Theory and Dynamical Systems: Decentralised Decision-Making and Spontaneous Order 4. Markov Chains and Stochastic Stability: Understanding Cultural Universals 5. Individual Threshold Models and Public Signals: Fads, Riots, and Revolutions 6. Social Networks and Graph Theory: Small World Effects and Social Change 7. Peer Effects and Spatial Game Theory: Local and Global Efficiency 8. Agent-Based Modelling: Cascades and Self-Organised Criticality 9. Chaos Theory: Non-Linear Dynamics and Social Complexity
"Drawing on a rich array of historical and contemporary examples, this book provides an introduction to dynamical systems theory and how it elucidates the complex interplay of political, economic, and social factors that give rise to social norms and institutions. The exposition is exceptionally clear and tailored to different levels of mathematical preparation. It will appeal to experts as well as students across the social sciences." -- H. Peyton Young, University of Oxford & London School of Economics, UK
"An interdisciplinary book on complexity, a guided tour through mathematical methods ranging from evolutionary game theory, dynamical systems, Markov chains and graph theory to bifurcations and chaos, with applications to nonlinear social sciences. A rigorous introduction delivered by an intriguing storytelling approach." -- Gian Italo Bischi, Professor of Applied Mathematics, University of Urbino, Italy