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


Relatore
Luciano Campi - Università di Milano

Data e ora
martedì 9 novembre 2021 alle ore 12.00 - In presenza + Zoom Webinar.

Referente
Alessandro Gnoatto

Data pubblicazione
30 settembre 2021

Dipartimento
Scienze Economiche  

Riassunto

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).

Personal Website https://sites.google.com/site/lucianocampi1/Home
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