Fictitious Play

Fictitious play is an iterative algorithm used to find Nash equilibria in games, particularly useful for multi-agent scenarios where players learn optimal strategies by repeatedly playing against estimations of their opponents' strategies. Current research focuses on extending fictitious play to more complex game settings, including mean-field games with heterogeneous players and multi-stage games, often incorporating deep reinforcement learning and optimistic variants for improved efficiency and convergence. These advancements are enabling the application of fictitious play to increasingly realistic and large-scale problems, such as those found in economics, operations research, and AI, with recent successes demonstrated in competitive game playing.