APDEs Seminar

We are interested in a class of spatial dynamic general equilibrium models that allows to take account of the micro-foundation of spatial factors’ allocation. We adopt a decentralized viewpoint, where each agent moves across the space maximizing its own utility which depends on the state of the other agents through an interaction term (influencing also the dynamic of the human capital). We set the problem into the framework of Mean Field Games (MFG), whose techniques are mostly based on partial differential equations and stochastic control, and were inspired by statistical physics to study Nash equilibria in differential games with a population of infinitely many identical players. The novelty of the MFG model we consider lies in the dependence of the human capital on the interactions among agents (e.g. spillovers) through an aggregation term. We study the well-posedness of the associated MFG system (with an infinite number of agents) depending on the strength of the aggregation term. Numerical experience is provided in some particular cases. This is a joint work with Cristiano Ricci and Giovanni Zanco.