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

Abstract: We study a Mean Field Game (MFG) model arising in Economics where each agent chooses its position in space and its level of human capital- i.e. the skills aimed at use in production possessed by each individual- and interacts with the other agents through the human capital. The main goal consists in studying the effect of spatial interaction terms (called in Economics spatial spillovers) on the abilities of each individual, due to the proximity, in terms of spatial distance, of other individuals. The resulting MFG system has a highly non standard structure, that is, a non-separable Hamiltonian and a non-monotone cost. In the talk we describe the economic model, we prove existence to the associated MFG system by a fixed point argument, and we provide some numerical experience. This is a joint work with F. Gozzi (LUISS, Italy) C. Ricci (Pisa, Italy), and G. Zanco (LUISS, Italy). The economic model has been developed through contributions by G. Fabbri (CNRS Grenoble), D. Fiaschi (Pisa, Italy), F. Gozzi (LUISS, Italy).