MAE 298 SEMINAR: A control-theoretic perspective on game-theoretic learning

Abstract: The framework of multi-agent game-theoretic learning explores how individual agent strategies evolve in response to the strategies of others. A central question is whether these evolving strategies converge to classical solution concepts, such as Nash equilibrium. This talk adopts a control-theoretic perspective by recognizing that learning agents interacting with one another form a feedback system. Learning dynamics are modeled as open dynamical systems that map payoffs, regardless of their source, into strategy updates, while the game itself provides the feedback interconnection. The focus is on uncoupled learning, where agents update strategies based solely on observed payoffs, without explicit knowledge of utility functions (their own or of others). This perspective enables the use of control-theoretic tools to both analyze and synthesize learning dynamics. We first exploit that convergence to Nash equilibrium corresponds to feedback stability. The main part of the talk establishes that uncoupled learning can, in general, lead to mixed-strategy Nash equilibrium, while highlighting that the required learning dynamics are not universal and may sometimes involve seemingly irrational behavior. We go on to show how a control-theoretic perspective supports compositional analysis of learning in games, i.e., accommodating hybrid learning dynamics and game structures, using game-theoretic extensions of passivity theory.

Bio: Jeff Shamma is department head of Industrial and Enterprise Systems Engineering and Jerry S. Dobrovolny Chair at the University of Illinois Urbana-Champaign. He previously held faculty positions at the King Abdullah University of Science and Technology (KAUST) and at Georgia Tech as the Julian T. Hightower Chair in Systems and Controls. Shamma received a doctorate in systems science and engineering from MIT in 1988. He is a fellow of IEEE and IFAC, a past Distinguished Lecturer of the IEEE Control Systems Society and a recipient of the IFAC High Impact Paper Award, AACC Donald P. Eckman Award and NSF Young Investigator Award. Shamma has been a plenary/semi-plenary speaker at NeurIPS, World Congress of the Game Theory Society, and IEEE Conference on Decision and Control. He was editor-in-chief of the IEEE Transactions on Control of Network Systems from 2020-2024. His research focuses on decision and control, game theory and multi-agent systems.