Markov Games: Concepts and Applications in Reinforcement Learning

This lecture introduces the concept of Markov games, a critical area in reinforcement learning. It begins with a historical overview of game theory, highlighting key figures such as John von Neumann and John Nash. The instructor explains normal form games, including their structure, equilibria, and dynamics, such as iterated best response and fictitious play. The discussion progresses to two-player games, emphasizing the prisoner's dilemma and zero-sum games, where one player's gain is another's loss. The lecture further explores response models, including best responses and softmax responses, and delves into Nash equilibria, illustrating their significance in game theory. The instructor also addresses the challenges of computing Nash equilibria, particularly in mixed strategies, and introduces algorithms for Markov games, including value iteration and policy gradient methods. Real-world applications, such as traffic interactions modeled as Markov games, are presented to illustrate the practical implications of these concepts. The lecture concludes with a summary of the key points discussed, reinforcing the importance of understanding Markov games in the context of reinforcement learning.