This presentation explores Mean Field Games (MFGs) on long-term regimes. We focus on the finite-state, infinite-horizon MFG problem with ergodic cost and Markovian strategies. Our main result proves that any solution to the MFG system corresponds to a (C/\sqrt{n})-Nash equilibrium in the n-player game, establishing a connection between MFGs and large-scale player interactions. We further extend this result to the strategy profile derived from the master equation. Additionally, we introduce a large deviation principle for the empirical measures of asymptotic Nash equilibria. Finally, we derive explicit forms for the rate functions in the two-dimensional case and compare the strategy profiles of the asymptotic Nash equilibria. This is a joint work with Ethan Zell and Ethan Huffman.

Short Bio:  Asaf Cohen is an Associate Professor in the Mathematics Department at the University of Michigan. He received his Ph.D. in Mathematics from Tel Aviv University. His research interests include the asymptotic analysis of complex systems, particularly queueing systems and mean field games. Recently, he has focused on developing machine learning tools for solving mean field games and is exploring long-term regimes in these systems.