A Mean Field Game model in economics with spatial interactions in the human capital

We study an economic model where each agent chooses its position in space and its level of human capital  maximizing its own utility and interacts with the other agents through the human capital. The main peculiarity  of the model we consider consists in the presence of a spatial interaction terms in the dynamic of the human capital, i.e. spatial spillovers on the accumulation of human capital and in the utility, i.e. spatial spillovers on the consumption.   We adopt a Mean Field Game (MFG) approach and study a system of two partial differential equations, the MFG system, which arises as the continuum macroscopic description of the discrete multi-agents system  emerging, heuristically, as the limit as the number of agents tends to infinity. The MFG system we study is expected to approximate  Nash equilibria for the discrete multi-agents system when the number of players tends to infinity. In this talk we explain our model, we provide existence to the MFG system and we apply the model to epidemiological models where the rate of transmission depends on the distribution of the population.

This is a joint work with C. Ricci (Pisa) and G. Zanco (LUISS). The economic model has been developed through contributions by G. Fabbri (CNRS Grenoble), D. Fiaschi (Pisa), and F. Gozzi (LUISS).