The book explores the innovative use of evolutionary game theory within social physics, illustrating its ability to quantitatively model complex interactions among human, environmental, and social systems. By merging mathematical frameworks with social science applications, it offers insightful perspectives on how these theories can enhance our understanding of societal dynamics.
Focusing on evolutionary game theory, this book explores its application to epidemic analysis, particularly relevant in the wake of the COVID-19 pandemic. It aims to provide a robust framework for modeling the spread of infectious diseases and understanding human decision-making during crises. By integrating a mathematical epidemiological model with a variant of the "vaccination game," it offers insights into social dynamics and presents an expanded concept of the vaccination game, addressing both foundational issues and contemporary practical applications.
Focusing on the 2-player, 2-strategy game, often referred to as the "2×2 game," the book explores its foundational theory and diverse applications across various fields, including engineering and social sciences. It delves into replicator dynamics and the discrepancies between theoretical models and real-world social systems, attributing these gaps to a mechanism called social viscosity. Additionally, it emphasizes network reciprocity as a crucial factor for fostering cooperation and provides practical examples, such as traffic flow analysis, illustrating the relevance of evolutionary game theory in understanding complex systems.
This book is for all graduate students who are specializing in any environmental issue and who wish to grasp the fundamentals of physics that are required in various fields of science and engineering. The book provides the structural concept of the system state equation and its dynamics, which can be applicable to numerical solutions in several important areas such as heat and mass transfer and fluid dynamics. As a first step, there is a description of how to solve a linear system by conducting an analysis of temperature distribution in an infinite soil as a practical example. This exercise helps readers to fully understand what time and space discretizations are, and how actual numerical solutions should work. Because the concept of the system state equation relies on a vector–matrix form, the book shows how that particular form is applicable to other practical procedures: linear multi regression analysis, the least square method, and others. The book also gives the solution to non-linear dynamical systems and their applications. Although this book may appear to take an unusual approach, the author believes it will be inspiring and greatly helpful for the beginner who seeks a solid understanding of the basis of mathematics and physics for any environmental problems.