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 an