Abstract

In the study of Mean Field Games (MFG), the Turnpike Property plays a crucial role in understanding the asymptotic behavior of large populations of agents. This property suggests that, for sufficiently long time horizons, the optimal trajectories of agents in a dynamic system converge to a steady-state or “turnpike” region, where their strategies remain approximately constant. The presence of the turnpike reflects the system’s tendency to stabilize and suggests that most of the time, agents will follow similar paths despite starting from different initial conditions.

In this introductory talk we investigate the turnpike property in the context of Lagrangian and Eulerian formulations of MFGs, which describe the agents either through their individual trajectories (Lagrangian) or through a distribution function over space (Eulerian). In both frameworks, we explore how the turnpike emerges and its implications for the long-term dynamics of the system, aiming at key applications in economics, control theory, and multi-agent systems.

The video of the seminar will appear shortly afterwards in this Mediaspace channel.

Seminario Dottorato