Department of Mathematical Sciences
Colloquium
Friday, October 3rd, 2025
11:00AM-11:50AM
Stratton Hall 202
Speaker: Jiamin Jian, University of Michigan
Title: Turnpike properties in linear quadratic Gaussian $N$-player differential games.
Abstract: We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By analyzing convergence toward the corresponding ergodic game, we establish exponential convergence estimates between the solutions of the finite-horizon Riccati system and the associated algebraic Riccati system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a turnpike property for the equilibrium pairs of each player. Importantly, our approach avoids reliance on the mean field game limiting model, allowing for a fully uniform analysis with respect to the number of players $N$. As a result, we further establish a uniform turnpike property for the equilibrium pairs between the finite-horizon and ergodic games with $N$ players.