Abstract: Diffusion of knowledge models in macroeconomics describe the evolution of an interacting system of agents who perform individual Brownian motions (this is internal innovation) but also can jump on top of each other (this is an agent or a company acquiring knowledge from another agent or company). The learning strategy of the individual agents (jump probabilities) are obtained from an additional optimization problem that involves the current configuration of particles and is a solution to a forward-backwards in time mean-field game. We will discuss some results on the basic properties of this system. This is a joint work with H. Berestycki, A. Novikov and J.-M. Roquejoffre.

Il seminario si svolgerà all'interno delle attività del progetto PRIN 2022W58BJ5 ``PDEs and optimal control methods in mean field games, population dynamics and multi-agent models'' finanziato dall'Unione europea - Next Generation EU.