Title: Mean Field Games and Applications
Abstract: Mean field game theory is a relatively new development in mathematics that helps us model situations with large numbers of rational agents. Its many applications are found in economics and finance, networks and cybersecurity, and even biology. In this presentation we introduce the fundamentals of the theory, starting with an explanation of the two conceptual components--game theory and mean field theory--and then putting them together. We will see how this leads to interesting mathematical models composed of nonlinear partial differential equations, and we will discuss some of the technical tools used to analyze them. Finally, we will present some of the latest results on mean field games and make some remarks on open problems.