Long-term Dynamics and Learning in Large Population Games

This project advances the mathematical foundations of mean field games, a powerful framework for modeling the collective behavior of large populations of strategic agents. While most existing research has focused on finite-horizon interactions, this project investigates the long-term dynamics of these systems, where questions of stability, equilibrium selection, and robustness are especially critical. Many real-world systems - such as communication networks, financial markets, and ecological populations - evolve over extended periods and require both coordination and long-run predictability. By analyzing how stable behavioral patterns emerge and persist in such settings, this research contributes to a deeper scientific understanding and supports the development of resilient technologies. The investigator aims to rigorously connect the long-horizon behavior of finite-agent stochastic games to their mean field counterparts. The project explores structural features of these games that remain stable as the number of agents grows, quantifying the long-run deviation from equilibrium. A learning framework is also developed to guide agents toward equilibrium behavior while adapting to unknown parameters, with particular attention to convergence rates and long-run regret. Furthermore, the project examines systems with multiple mean field equilibria, developing probabilistic tools and numerical methods based on large deviations and deep learning, to describe metastable behaviors and transitions between equilibria. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.