Generalized Nash Equilibrium Seeking in Population Games: Applications the Control of Large Scale Multi agent Systems

This book is a comprehensive, self-contained guide to generalized Nash equilibrium (GNE) seeking methods for population games focused on optimizing the control of large-scale complex systems (LSCSs). It equips readers with the tools needed to model and solve non-cooperative multi-agent interactions using GNE methods. This provides a novel framework for tackling real-world problems like congestion management, energy systems, and dynamic resource allocation. The approaches in this book will benefit both researchers and practitioners because, by framing optimization-based control tasks as GNE problems and relying on the population games framework, they enable more robust, scalable solutions to challenges involving LSCSs. The book is structured to guide readers from foundational concepts such as variational inequalities and dissipativity theory, to advanced topics like the design of evolutionary and payoff dynamics models for distributed systems. The clear progression from theory to application is enhanced by numerous hands-on examples and fully documented Python code allowing readers to replicate and customize the book’s simulations for deeper understanding. Features of the text include: detailed illustrations of theoretical concepts, solutions to practical problems and a unique focus on integrating game theory with optimization-based control. This blend of rigorous theory and practical application makes this book a valuable resource for both students and professionals in the field of control systems and multi-agent decision-making.