Abstract:
The mean-field theory of Nash equilibria, developed by J.-M. Lasry and P.-L. Lions since 2006, leads to the analysis of systems of PDEs (Partial differential equations) where Hamilton-Jacobi and Fokker-Planck equations are coupled; the individual decisions are intimately connected with the distribution function describing mass evolution. I will present the background of this theory and the main challenges in terms of PDEs, then I will focus on specific applications to economic growth models based on knowledge exchange and diffusion.