Special Session 184: Mean-Field Games: From Partial Differential Equations to Numerical Methods

On the Local Turnpike Property in Mean Field Control and Games
Nicol\`o De Bernardi
Universit\`a degli Studi di Padova
Italy
Co-Author(s):    Marco Cirant
Abstract:
We study the local stability of solutions to ergodic and discounted Mean Field Games systems around stationary equilibria with quadratic Hamiltonians. Inspired by finite-dimensional models, we introduce a new stability assumption which allows for non-monotone local couplings, and show that this weaker condition still ensures a (local) exponential turnpike property for solutions close to the stationary one. We also provide an interpretation of this non-monotonicity assumption in terms of spectral properties of an operator, which might be encoded in the MFG system. This leads to a class of meaningful examples of MFG systems with no monotonicity but still fulfilling our new assumption. This talk is based on joint work with M. Cirant (Padova).