Student Analysis Seminar

We take a first look at a problem in mathematical game theory, formulated as an optimal control problem in continuous time. In this context, we introduce the foundational notions of Nash equilibrium and Hamilton-Jacobi-Bellman equations. Then, when considering large-player systems, we pose the abstraction of sending the number of players n\to\infty and formulate the so-called mean field game that arises. Finally, we mention the notion of equilibrium in the mean-field game and demonstrate how it naturally corresponds to the finite-player Nash equilibrium. This talk is based on joint work with Asaf Cohen. Speaker(s): Ethan Zell (University of Michigan)