Dynamic Games: Backward Induction and Nash Equilibria

This lecture focuses on dynamic games, particularly two-player zero-sum games, and the application of backward induction to find Nash equilibria. The instructor begins with a recap of previous concepts, emphasizing the importance of understanding the dynamics of state evolution and action spaces. The lecture outlines the basic elements of dynamic games, including stages, state spaces, and outcome functions. It introduces the concept of backward induction, explaining how it can be used to determine optimal strategies in a finite horizon setting. The instructor discusses the Bellman's Principle of optimality and its implications for single-player cases before extending the discussion to two-player scenarios. The lecture also covers the linear quadratic regulator (LQR) problem, illustrating how to derive Nash equilibria in this context. Throughout the session, the instructor encourages questions and clarifies complex concepts, ensuring that students grasp the intricacies of dynamic game theory and its applications in real-world scenarios.