Abstract

The term “turnpike” first appeared in econometrics in the 1950s, although the phenomenon had been observed by Von Neumann in 1938. It describes a stability property of optimal trajectories: the optimal path between any two points is the one that moves rapidly from the initial condition toward a steady state (the “turnpike”), remains close to it for most of the time horizon, and adjusts to meet the terminal condition only near the final time, provided the endpoints are sufficiently far apart. This property has been established in various contexts, including control theory, dynamical systems and Mean Field Games, under some suitable monotonicity assumptions on the model.

In this talk we will present some basic examples of turnpike properties, with the aim of highlighting the main structural features of the models that ensure their validity. Moreover, in the context of quadratic MFG, we will introduce a weaker monotonicity assumption that still guarantees the turnpike behavior toward local equilibria, along with an interpretation in terms of spectral properties of an operator encoded in the MFG system.

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

Seminario Dottorato