Orateur
Description
The question under study, at large intermediate times, of a system,
proposed by the economists Lucas and Moll, aimed at describing the growth of an economy by means of diffusion of knowledge. The individual agents in the economy are supposed to share their time between learning and producing. They advance their knowledge by
learning from each other and via internal innovation, and their density obeys a forward in time equation of reaction-diffusion type. The learning strategy of the agents is based on the solution to a backward in time nonlocal Hamilton-Jacobi-Bellman equation that is
coupled to the equation for the agents density. The result is a system of the mean-field game type. An important parameter, that measures how successful the learning is, determines different asymptotic regimes. One of them, that does not
seem to have been identified in the literature, where most of the
agents spend almost all their time to learn, and whose large
intermediate time behaviour has a lot to do with Fisher-KPP
propgation, will be especially discussed.
Joint work with H. Berestycki, A. Novikov, L. Ryzhik
