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

Luciano Campi; Matteo Burzoni

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

Matteo Burzoni, Luciano Campi

Probability · Submitted 1 Jul 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.55	0.62	0.07	asserted 0.96
s1	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.	result 0.82	0.96	0.61	asserted 1.00
s2	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.	method 1.00	0.96	0.09	asserted 1.00
s3	We exploit these ideas also to construct $\varepsilon$-Nash equilibria for the $N$-player game.	contribution 0.67	0.95	0.11	asserted 1.00
s4	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.	method 0.54	0.32	0.04	asserted 0.85
s5	We also introduce and discuss a novel model of bank run that can be studied within this framework.	contribution 0.99	0.92	0.09	asserted 0.85

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Original 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.

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7 arXiv papers cite this in 10 sentences

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Compares with it 1 paper

Second, in contrast to [ref] , where the coefficients of the players' processes may depend on the loss process and to [ref] , which further includes a driver which is a smoothed version of $L$ (hence modeling delayed effects of hitting the boundary), we consider the firm values driven by $L$ directly, resulting in an instantaneous effect of defaults and the emergence of systemic events.

Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem · Contributions and findings · 1.00

Cites it as background 3 papers

The theory on mean-field games with regular control and absorption has received a lot of interest recently, being developed in [ref] , and using the linear programming approach in [ref] .

Linear Programming Fictitious Play algorithm for Mean Field Games with optimal stopping and absorption · Introduction · 0.89
A model for bank runs with common noise and smooth transmission of boundary losses was analysed in [ref] .

Contagious McKean--Vlasov problems with common noise: from smooth to singular feedback through hitting times · Introduction · 0.92
Specific stochastic MFGs with absorption have been considered by, e.g. Campi and coauthors in [ref] .

Mean-Field Liquidation Games with Market Drop-out · Introduction · 0.91

What it cites

Cites as background 1 paper

For a recent survey of the many applications of such a class of games, especially in economics and finance, we refer to [ref] .

Applications of Mean Field Games in Financial Engineering and Economic Theory · Introduction · 0.99

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