Convex Games: Applications and Equilibria

This lecture focuses on convex games, beginning with an introduction to classical games such as Cournot and Bertrand competitions. The instructor discusses the formulation of convex games and the significance of Kakutani's fixed point theorem in establishing the existence of equilibria. The lecture also covers the variational inequality characterization of Nash equilibria and the uniqueness of these equilibria. Various applications of convex games are highlighted, including their relevance in traffic networks, electricity markets, and communication networks. The instructor emphasizes the importance of understanding these concepts through practical examples and problem-solving exercises. The lecture aims to provide a comprehensive overview of convex games, their theoretical foundations, and their applications in real-world scenarios, making it a crucial part of the course on multiagent learning and control.