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 emphasisesboth 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.
Author(s): Sebastian Ille
Publisher: Routledge
Year: 2022
Language: English
Pages: 276
City: London
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Figures
List of Tables
Chapter 1: Introduction
1.1 Aim and Scope
1.2 Some Caveats
1.3 For Whom Is This Book and How to Use It?
1.4 Acknowledgement
Chapter 2: Game Theory: Strategic Interactions
2.1 Introduction
2.2 Definition of a Game
2.3 The Ultimatum Game
2.4 Signalling, Focal Points, and Practices
2.5 Strategic Complements and Substitutes
2.6 Conclusion: The Limits of Game Theory
Chapter 3: Evolutionary Game Theory and Dynamical Systems: Decentralised Decision-Making and Spontaneous Order
3.1 Introduction
3.2 The Continuous Replicator Model
3.3 Regime Change, Stability and Bifurcation
3.4 Multi-Population and N-Strategy Games
3.5 Three Strategies with One and Two Populations
3.6 Conclusion
Chapter 4: Markov Chains and Stochastic Stability: Understanding Cultural Universals
4.1 Introduction
4.2 Markov Chains
4.3 Stochastic Stability
4.4 Benefit and Caveats
4.5 Loss Sensitivity and Idiosyncratic Errors
4.6 Conclusion
Chapter 5: Individual Threshold Models and Public Signals: Fads, Riots, and Revolutions
5.1 Introduction
5.2 Thresholds in a Single Population
5.3 Thresholds in More Than One Population
5.4 Two Populations with Uniform Distributions
5.5 Extensions with Individual Preferences and Choices
5.6 Conclusion
Chapter 6: Social Networks and Graph Theory: Small World Effects and Social Change
6.1 Introduction
6.2 Definitions and Elementary Measures
6.3 Centralities
6.4 Application
6.5 Preferential Attachment and the Power Law
6.6 Conclusion
Chapter 7: Peer Effects and Spatial Game Theory: Local and Global Efficiency
7.1 Introduction
7.2 Local Imitation on Regular Networks
7.3 Non-Symmetric Interactions and Payoff vs. Imitation Space
7.4 Other Spatial Games
7.5 Extension: Co-evolving networks
7.6 Conclusion
Chapter 8: Agent-Based Modelling: Cascades and Self-Organised Criticality
8.1 Introduction
8.2 Critical Systems
8.3 Complexity, Criticality, and ABM
8.4 Segregation
8.5 Self-Organised Criticality
8.6 Conclusion
Chapter 9: Chaos Theory: Non-Linear Dynamics and Social Complexity
9.1 Introduction
9.2 Threshold Models with Decision Reversals
9.3 An Information Spin Glass
9.4 Chaos in Evolutionary Games
9.5 Conclusion
Appendix A
A.1 Elementaries
A.2 Equilibrium Refinements and Discrimination Criteria
A.3 Derivation of the Replicator Dynamics
A.4 Extensions of the Replicator Dynamics
A.5 Dynamical Systems Revisited
A.6 Solving the Roots of Polynomials
A.7 Deriving Modularity
Bibliography
Index
