Mean field games with absorption and common noise with a model of bank run

Supervisor
Luciano Campi - Università di Milano

Date and time
Tuesday, November 9, 2021 at 12:00 PM - In presenza + Zoom Webinar.

Contact person
Alessandro Gnoatto

Publication date
September 30, 2021

Department
Economics

Summary

Abstract: We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state space. We provide a general result for the existence of weak mean field equilibria which, due to the absorption and the common noise, are given by random flow of sub-probabilities. We first use a fixed point argument to find solutions to the mean field problem in a reduced setting resulting from a discretization procedure and then we prove convergence of such equilibria to the desired solution. We exploit these ideas also to construct $\varepsilon$-Nash equilibria for the $N$-player game. Since the approximation is two-fold, one given by the mean field limit and one given by the discretization, some suitable convergence results are needed. We also introduce and discuss a novel model of bank run that can be studied within this framework.This talk is based on a joint paper with Matteo Burzoni (University of Milan).