Abstract:

Stochastic differential games with mean field interaction, when the number of players is very large. In this sense, computing an equilibrium for the mean field game allows one to construct approximate Nash equilibria for the finite-player game, with an error that vanishes as the number of players grows. In the first part of the talk, I will discuss the main ideas behind this class of models. In the second part, I will focus more specifically on a mean field game model of bank runs, in which a continuum of depositors is invested in a risky project and can decide if and when to withdraw. Such a model exhibits strategic complementarities, and multiple equilibria may arise. The existence of equilibria is established via Tarski’s fixed-point theorem, and they can be computed using numerical algorithms. Uniqueness can be restored in the presence of common noise.