Mean Field Games in Economics
Tuesday, November 13, 2012 - 11:20am - 12:20pm
Mean field games are everywhere in economics. Why? Because heterogeneity is everywhere. For example, macroeconomists often use heterogeneous agent models to understand the interactions between income and wealth distribution and aggregates like GDP. Classic examples are papers by Aiyagari (1994) and Krusell and Smith (1998). But the mathematical structure of these models is not well understood and numerical solution often resorts to somewhat awkward approximation techniques. These models are really mean field games: Individuals optimize taking as given the evolution of the wealth distribution (HJB equation), and the evolution of the wealth distribution is determined by individual savings behavior (Kolmogorov Forward Equation). I argue that there should be high payoffs from well-trained mathematicians working on issues of numerical solution, existence and uniqueness. I will also present a Boltzmann mean field game that came up in some of my own research (Lucas and Moll, 2012).